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ASVAB Total Prep 2022–2023 7 Practice Tests + Proven Strategies + Video + Flashcards (Kaplan Test Prep)

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ASVAB
TOTAL PREP
2022–2023
Our 80 years’ expertise = Your competitive advantage
7 Practice Tests + Proven Strategies + Video + Flashcards
ACKNOWLEDGMENTS
Editor, 2022–2023 edition
Paula L. Fleming, MA, MBA
Special thanks to Matt Belinkie, Brian Carlidge, Michael Collins, Lola Disparte, Joanna Graham,
Allison Harm, Craig Harman, Jack Hayes, Rebecca Houck, Melissa McLaughlin, Camellia
Mukherjee, Rachel Pearsall, Tammi Rice, Anne Marie Salloum, Amit Schlesinger, Gordon Spector,
Sascha Strelka, Bonnie Wang, Ethan Weber, Michael Wolff, and many others.
This publication is designed to provide accurate information in regard to the subject matter
covered as of its publication date, with the understanding that knowledge and best practice
constantly evolve. The publisher is not engaged in rendering medical, legal, accounting, or other
professional service. If medical or legal advice or other expert assistance is required, the services
of a competent professional should be sought. This publication is not intended for use in clinical
practice or the delivery of medical care. To the fullest extent of the law, neither the Publisher nor
the Editors assume any liability for any injury and/or damage to persons or property arising out of
or related to any use of the material contained in this book.
© 2021 by Kaplan, Inc.
Published by Kaplan Publishing, a division of Kaplan, Inc.
750 Third Avenue
New York, NY 10017
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storage and retrieval system, in any form or by any means, whether electronic or mechanical, now
known or hereina er invented, without the express written permission of the publisher.
10 9 8 7 6 5 4 3 2 1
ISBN: 978-1-5062-7917-6
Kaplan Publishing books are available at special quantity discounts to use for sales promotions,
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call the Simon & Schuster Special Sales department at 866-506-1949.
Table of Contents
Foreword
Welcome to Your ASVAB Studies!
Your Kaplan Resources
Three Levels of Study
Getting Started
Managing Stress
Final Preparations for Test Day
Good Luck!
Chapter 1: About the ASVAB
What Is the ASVAB?
What Does the ASVAB Test?
What Is the AFQT?
Your AFQT Score
AFQT Qualifying Scores for Different Branches
of the Military
ASVAB Logistics
Registering for and Taking the ASVAB
How to Read Your ASVAB Scores
Different Versions of the ASVAB
The Paper-and-Pencil Test vs. the CAT
Kaplan’s ASVAB Strategies
CAT-ASVAB Strategies
Getting Ready for the ASVAB
Chapter 2: ASVAB Diagnostic Tests
About The Diagnostic Test
ASVAB Diagnostic Test
Part 1: General Science (GS)
Part 2: Arithmetic Reasoning (AR)
Part 3: Word Knowledge (WK)
Part 4: Paragraph Comprehension (PC)
Part 5: Mathematics Knowledge (MK)
Part 6: Electronics Information (EI)
Part 7: Auto and Shop Information (AS)
Part 8: Mechanical Comprehension (MC)
Part 9: Assembling Objects (AO)
ASVAB Diagnostic Test Answers and
Explanations
Part 1: General Science (GS): Answers and
Explanations
Part 2: Arithmetic Reasoning (AR): Answers and
Explanations
Part 3: Word Knowledge (WK): Answers and
Explanations
Part 4: Paragraph Comprehension (PC): Answers
and Explanations
Part 5: Mathematics Knowledge (MK): Answers
and Explanations
Part 6: Electronics Information (EI): Answers and
Explanations
Part 7: Auto and Shop Information (AS): Answers
and Explanations
Part 8: Mechanical Comprehension (MC):
Answers and Explanations
Part 9: Assembling Objects (AO): Answers and
Explanations
Chapter 3: Word Knowledge
Know What to Expect
The Kaplan Method For Word Knowledge
Questions
Decoding Strategies For Guessing A Word’s
Meaning
Breaking Words Apart
Prefixes
Suffixes
Greek and Latin Word Roots
Practice with Word Roots
Using Positive or Negative Charge
Using Real-World Context to Guess at a Word’s
Meaning
Making the Most of Context
Eliminating Answer Choices Based on Logic
Strategies for Building Your Vocabulary
Word Knowledge Practice Set 1
Word Knowledge Practice Set 2
Answers and Explanations, Practice Set 1
Answers and Explanations, Practice Set 2
Review and Reflect
Chapter 4: Paragraph Comprehension
Know What to Expect
The Kaplan Method for Paragraph
Comprehension Questions
Conquering Paragraph Comprehension
Questions
Global Questions
Detail Questions
Inference Questions
Vocabulary-in-Context Questions
Paragraph Comprehension Practice Set 1
Paragraph Comprehension Practice Set 2
Answers and Explanations, Practice Set 1
Answers and Explanations, Practice Set 2
Review and Reflect
Chapter 5: Math Strategies for the ASVAB
Know What to Expect
The Kaplan Method for ASVAB Math Questions
Strategies for Solving Math Problems
Backsolving
Picking Numbers
Strategic Guessing Using Logic
Combination of Approaches
Math Strategies for the ASVAB Practice Set
Answers and Explanations
Review and Reflect
Chapter 6: Arithmetic Reasoning
Know What to Expect
Arithmetic Review
Arithmetic Definitions
Number Properties
Absolute Value
Factors, Multiples, and Prime Numbers
Divisibility
Fractions and Decimals
Decimal Division
Exponents and Radicals
Factorials
Applied Arithmetic Review
The Order of Operations
Distributive and Commutative Properties
Ratios, Proportions, and Rates
Combined Work
Percent Problems
Statistical Terms
Sequences
Probability
Arithmetic Word Problems
Translation
Word Problems with Formulas
Arithmetic Reasoning Practice Set 1
Arithmetic Reasoning Practice Set 2
Answers and Explanations, Practice Set 1
Answers and Explanations, Practice Set 2
Review and Reflect
Chapter 7: Mathematics Knowledge
Know What to Expect
Algebra Review
Terms and Expressions
Equations with One Variable
Equations with Two Variables
Systems of Equations
Quadratic Equations with Variables
Inequalities
Geometry Review
Lines and Angles
Polygons
Circles
Solid Geometry
Combined Figures
Coordinate Geometry
Mathematics Knowledge Practice Set 1
Mathematics Knowledge Practice Set 2
Answers and Explanations, Practice Set 1
Answers and Explanations, Practice Set 2
Review and Reflect
Chapter 8: Conquering the Technical Subtests
The Kaplan Method for ASVAB Technical
Subtest Questions
Bringing It All Together
Final Thought Before You Dive In
Chapter 9: General Science
Know What to Expect
PART I: LIFE SCIENCE
Nutrition and Health
Human Body Systems and Diseases
The Skeleton and Muscles
The Respiratory System
Blood and the Circulatory System
The Digestive and Excretory Systems
The Nervous System
The Reproductive System
Human Pathogens
Genetics
Cellular Structures and Functions
Ecology
The Classification of Living Things
Life Science Practice Questions
Answers and Explanations
PART II: EARTH AND SPACE SCIENCE
Geology
Structure of Earth
Plate Tectonics
Types of Rocks
Geologic Time Scale
Cycles in Earth Science
Meteorology
Earth’s Atmosphere
Fronts
Clouds
Our Solar System
The Sun
The Planets and Other Phenomena
Earth and Space Science Practice Questions
Answers and Explanations
PART III: PHYSICAL SCIENCE
Measurement
Physics
Motion
Forces and Energy
Newton’s Laws
Energy
Sound Waves
The Electromagnetic Spectrum
Optics
Heat
Magnetism
Chemistry
Elements and the Periodic Table
Compounds
Acids and Bases
Physical Change
Chemical Change
Physical Science Practice Questions
Answers and Explanations
PART IV: GENERAL SCIENCE PRACTICE
QUESTIONS
General Science Practice Set 1
General Science Practice Set 2
Answers and Explanations, Practice Set 1
Answers and Explanations, Practice Set 2
Review and Reflect
Chapter 10: Electronics Information
Know What to Expect
Electron Flow Theory
Current
Voltage
Resistance
Exceptions and Additional Notes
Circuits
Ohm’s Law
Series Circuits
Parallel Circuits
Series-Parallel Circuits
Electrical Power
Standard Electrical Units and the Metric System
Structure of Electrical and Electronic Systems
AC vs. DC
Ground
Important Electric and Electronic Components
Semiconductors
Diodes
Transistors
Electricity and Magnetism
Inductors
Transformers
Basic Electrical Motors and Generators
Electronics Information Practice Set 1
Electronics Information Practice Set 2
Answers and Explanations, Practice Set 1
Answers and Explanations, Practice Set 2
Review and Reflect
Chapter 11: Automotive Information
Know What to Expect
What’s in This Chapter
Engine Systems
Basic Engine Theory
Cooling System
Lubrication System
Combustion Systems
Fuel System
Ignition System
Exhaust Systems
Electrical and Control Systems
Electrical System
Computer System
Chassis Systems
Drivetrain System
Suspension and Steering System
Brake Systems
Auto Information Practice Set 1
Auto Information Practice Set 2
Answers and Explanations, Practice Set 1
Answers and Explanations, Practice Set 2
Review and Reflect
Chapter 12: Shop Information
Know What to Expect
Measuring Tools
Tape Measures and Steel Rules
Micrometers
Calipers
Spirit Levels
Steel Squares
Striking Tools
Hammers
Nails
Rivets
Chisels, Punches, and Drifts
Turning Tools
Screwdrivers
Wrenches
Sockets
Nuts and Bolts
Fastening Tools
Ring Fasteners
Soldering Tools
Welding Tools
Gripping Tools
Pliers
Clamps
Vises
Cutting Tools
Manual (Hand) Saws
Powered Saws
Drilling and Boring Tools
Finishing Tools
Planes
Wood Chisels
Files and Rasps
Shop Information Practice Set 1
Shop Information Practice Set 2
Answers and Explanations, Practice Set 1
Answers and Explanations, Practice Set 2
Review and Reflect
Chapter 13: Mechanical Comprehension
Know What to Expect
A Review of the Physics of Mechanical Devices
Mass and Force
Newton’s Laws of Motion
Common Types of Forces
Gravity and Weight
Friction
Tension
Hydraulic Pressure
Torque
Energy, Work, and Power
Energy
Work
Power
Simple Machines
Inclined Plane
Wedge
Levers
Pulleys
Block and Tackle
Wheel and Axle
Gears and Gear Ratios
Mechanical Comprehension Practice Set 1
Mechanical Comprehension Practice Set 2
Answers and Explanations, Practice Set 1
Answers and Explanations, Practice Set 2
Review and Reflect
Chapter 14: Assembling Objects
Know What to Expect
Jigsaw-Puzzle-Type Problems
Connector-Type Problems
Assembling Objects Practice Set 1
Assembling Objects Practice Set 2
Answers and Explanations, Practice Set 1
Answers and Explanations, Practice Set 2
Review and Reflect
Chapter 15: ASVAB Practice Tests
ASVAB Practice Test A
Part 1: General Science (GS)
Part 2: Arithmetic Reasoning (AR)
Part 3: Word Knowledge (WK)
Part 4: Paragraph Comprehension (PC)
Part 5: Mathematics Knowledge (MK)
Part 6: Electronics Information (EI)
Part 7: Auto and Shop Information (AS)
Part 8: Mechanical Comprehension (MC)
Part 9: Assembling Objects (AO)
ASVAB Practice Test A Answers and
Explanations
Part 1: General Science Answers and
Explanations
Part 2: Arithmetic Reasoning Answers and
Explanations
Part 3: Word Knowledge Answers and
Explanations
Part 4: Paragraph Comprehension Answers and
Explanations
Part 5: Mathematics Knowledge Answers and
Explanations
Part 6: Electronics Information Answers and
Explanations
Part 7: Auto and Shop Information Answers and
Explanations
Part 8: Mechanical Comprehension Answers and
Explanations
Part 9: Assembling Objects Answers and
Explanations
ASVAB Practice Test B
Part 1: General Science (GS)
Part 2: Arithmetic Reasoning (AR)
Part 3: Word Knowledge (WK)
Part 4: Paragraph Comprehension (PC)
Part 5: Mathematics Knowledge (MK)
Part 6: Electronics Information (EI)
Part 7: Auto and Shop Information (AS)
Part 8: Mechanical Comprehension (MC)
Part 9: Assembling Objects (AO)
ASVAB Practice Test B Answers and
Explanations
Part 1: General Science Answers and
Explanations
Part 2: Arithmetic Reasoning Answers and
Explanations
Part 3: Word Knowledge Answers and
Explanations
Part 4: Paragraph Comprehension Answers and
Explanations
Part 5: Mathematics Knowledge Answers and
Explanations
Part 6: Electronics Information Answers and
Explanations
Part 7: Auto and Shop Information Answers and
Explanations
Part 8: Mechanical Comprehension Answers and
Explanations
Part 9: Assembling Objects Answers and
Explanations
Appendix: Word Parts
Part I: Prefixes
Part II: Suffixes
Part III: Word Roots
ASVAB Verbal Strategy Sheet
ASVAB Math Strategy Sheet
Flashcards
FOREWORD
Congratulations on taking an important step toward enlisting in one of the
United States Armed Services! The Air Force, Army, Coast Guard, Marines,
Navy, and National Guard all emphasize the importance of mission
preparedness. By obtaining this Kaplan ASVAB book, you are on your way
toward being well prepared to take the ASVAB test that is a prerequisite for
enlisting in one of the services. The United States Military Entrance
Processing Command administers the ASVAB for all the services. That
organization calls the enlistment process “Freedom’s Front Door.”
The Armed Services give our marines, sailors, soldiers, guardsmen and women, and airmen and -women the opportunity to grow personally and
professionally, to assume major responsibilities, and to work in integrated
teams to achieve their goals. The military needs bright, talented young
individuals to serve our country, and the ASVAB is one of the factors used
to enlist the most qualified applicants. Being selected for the military is
very competitive; not only do you have to meet certain threshold
standards, including ASVAB scores, but you are also competing with
thousands of other applicants for these coveted openings.
My efforts as a member of the team that prepares new editions of the
Kaplan ASVAB book have brought back many memories of my four and a
half years as a proud member of the U.S. Navy. When I was in the
engineering department on a destroyer, an unusual combination of
circumstances resulted in our ship being about 40 percent below the
proper staffing level just three months before we were scheduled for a
major deployment. Our crew had to be augmented quickly, but, as the
saying goes, it takes three years to get three years’ experience.
Consequently, sailors just graduating from advanced training (“A School”
in Navy parlance) were slotted into positions on our ship normally staffed
by third-class petty officers with two or so years under their belts and
sometimes even second-class petty officers who might have been in their
second term of enlistment.
Fortunately, almost all of our new crew members were well suited for their
shipboard duties thanks, in part, to the version of the ASVAB that was
being used at that time. Consequently, they learned quickly and assumed
their responsibilities well. During their first full year on board, we were
deployed 290 days and we never missed a beat. In fact, many of us were
awarded the Navy Commendation Medal for restaffing so successfully that
we even covered a couple of operational commitments for other ships.
Needless to say, my experience convinced me that the process of selecting
the right people for the right jobs was very well executed. I made many
lifetime friendships in the Navy, and I have stayed in touch with some of
my shipmates since I le . Some went on to very successful careers in the
Navy. Several others used the G.I. Bill to help further their education and
went on to civilian careers.
Enough of my reminiscing! I mention my experiences to encourage you to
get the most that you can from this Kaplan ASVAB book so that you score
up to your maximum potential and are selected for the service and
occupational specialty that you want and that will enable you to excel.
Kaplan is the premier test preparation company in the world, and we have
applied our expertise and experience to this new edition. Because practice
is so important to your preparation, we have included three full-length
practice ASVAB tests in this book and scores of practice problems and
explanations. Your purchase of this book will also give you access to
Kaplan’s online resources, including four computer-based ASVAB practice
tests, 1,000 more practice questions, and videos covering key concepts.
When you complete an online test, your Performance Summary will give
you a detailed performance breakdown by skill or concept.
You have chosen the right tool to help you score as high as possible on the
ASVAB; the rest is up to you. Merely reading the book might help some, but
the real payoff will come from studying the material, taking the practice
assessments, and focusing on the areas where you can realize the most
improvement. Remember, your hard work will pay off with rewards on Test
Day and beyond! I wish you the best as you begin your journey and hope
that you find your time in the military as rewarding as I did.
Jack Hayes
Former LT., USN (and a former recruiter)
WELCOME TO YOUR ASVAB
STUDIES!
Thank you for choosing Kaplan to help you study for the ASVAB! We are
honored to be part of your preparation for a military career. Your Kaplan
book and online resources contain all the tools you need to succeed on
Test Day and earn your place in a branch of the armed services.
YOUR KAPLAN RESOURCES
Your Kaplan book contains:
a full-length diagnostic test
tools to help you plan your studies
chapters that cover each of the ASVAB subject tests, including:
Kaplan Methods for every question type
worked examples that display the expert approach
practice questions with explanations
two more full-length practice tests
500 flashcards to help you remember important concepts for the
technical subtests
Your Kaplan online resources offer:
40 instructional videos with key test-taking strategies
four additional full-length practice tests, to prepare you for Test Day
a Qbank with 1,000 items, to help you hone your skills
Performance Summaries, to help you keep track of your strengths and
areas of opportunity
Kaplan's flashcard app, so you can drill with your cards on any device
Between the Kaplan book and online resources, you have over 1,300
practice items at your disposal, as well as multiple tools to help
personalize your studies to your individual needs. In other words, you have
the resources you’ll need to achieve your goals on the ASVAB.
THREE LEVELS OF STUDY
Perhaps you’re already pretty good at the ASVAB, but you need to brush up
on specific skills or to review all of the skills lightly before Test Day. Or
maybe you feel moderately confident about the ASVAB, but you need
significant review on some or all of the topics. Or perhaps, like many
people, you’ve forgotten much of what you learned in high school and
need a comprehensive review.
Kaplan’s book and online resources will help you prepare for the ASVAB
regardless of which of those groups you fall into. The chart below outlines
three approaches you might take depending on your needs. Of course,
your individual situation may be best served by a combination of these
approaches.
If you need a quick brush-
If you need a moderate review
If you need to (re)learn
up or light overall review . .
of some or all of the topics . . .
many of the skills from
.
scratch . . .
Start by devoting one week to
Use the results from your
Give yourself plenty of
each of the subject tests.
diagnostic to identify your areas
time to work through this
During each of those weeks,
of greatest need. Start by
book, chapter by chapter.
read the appropriate chapter
devoting two weeks to each of
Periodically review the
and do the practice items in
those subject tests. During each
earlier chapters so that
the book.
of those weeks, read the
those skills stay fresh.
appropriate chapter and do the
practice items in the book.
A er you’ve completed your
A er you’ve done so, take a full-
Don’t take many full-
comprehensive review, take a
length test in the book or online
length tests until you’ve
full-length test in the book or
to gauge your progress.
reviewed most of the
online. If you haven’t seen
Continue to study and take a full-
subject tests. In the last
significant improvement,
length test every week or two,
few weeks before Test
continue to work on the
depending on your Test Day. In
Day, take a full-length
areas you find most
the last few weeks before Test
practice test (either in the
challenging. Take another
Day, give a week or several days
book or online) once a
full-length test every week or
to each of the subtests on which
week or once every two
two, depending on your test
you were already strong.
weeks, depending on
date.
GETTING STARTED
How To Get Started
1. Register your Kaplan online resources.
your test date.
2. Take the diagnostic test in your Kaplan book.
3. Review your performance and read through the explanations.
4. Contact a recruiter and do some research about your desired
military career.
5. Learn, practice, review.
6. Take full-length practice tests in your Kaplan book and in your
online resources.
1. Register your Kaplan online resources.
To obtain access to your Kaplan online resources, visit
kaptest.com/booksonline. Create your account by choosing "ASVAB,"
selecting your Kaplan ASVAB book, and answering the question or
questions that appear.
Once you have created your username and password, log in to your
resources at kaptest.com/login. Enter your username and password. Click
on the title of your book to see your resources.
2. Take the diagnostic test in your Kaplan book.
Chapter 2 of this book offers a full-length diagnostic test. As a first step in
your studies, set aside about three uninterrupted hours when you can take
the diagnostic test. Work through the subject tests in the order they’re
presented, with one break at most.
3. Review your performance and read through the
explanations.
A er you’ve taken the complete diagnostic test, check your answers using
the explanations that appear immediately a er the tests. When you check
your answers, don’t just check whether you got the question right or not.
Rather, read the explanations for all the questions. That’s because you can
learn a great deal from reviewing questions you’ve already done, even if
you got those questions right. As you review your performance on the
diagnostic, really think about why the right answers are right, why the
incorrect answers are incorrect, and what drew you to the answer you
chose.
4. Contact a recruiter and do some research.
You’re going to want to set some goals regarding your ASVAB score, but
different enlistees will have different priorities in studying for the ASVAB,
depending on their career aspirations. For example, a test taker who wants
to go into a technical career (such as equipment or computer technician)
will likely need high scores in Word Knowledge, Paragraph
Comprehension, Mathematics Knowledge, Arithmetic Reasoning, General
Science, and Mechanical Comprehension. However, a test taker who wants
to go into a career repairing structures or vehicles should likely emphasize
Auto and Shop Information, Electronic Information, and Mechanical
Comprehension over General Science.
Your recruiter is the best source of information about careers in the military
and the scores you will need to earn to be competitive for those careers.
Use information from your recruiter as well as information available on the
various branches’ websites to inform your ASVAB score goals.
5. Learn, practice, review.
Once you have taken your diagnostic and established some goals regarding
your ASVAB score, you’re ready to get down to serious studying. Effective
studying has three phases: learn, practice, review.
Learn: Each subject test on the ASVAB has its own chapter in this book.
Read these chapters carefully, paying particular attention to these features:
Concepts are introduced with learning objectives. Use these learning
objectives as a checklist of skills, to keep track of which you have
mastered and which you need to work on more.
Key terms you’ll need to understand are introduced in bold type.
Important strategies, takeaways, and shortcuts are highlighted in gray
boxes sprinkled throughout the book.
Worked examples appear throughout the book: each one shows, stepby-step, how an expert test taker would approach ASVAB questions.
Practice: Practice items are sprinkled throughout each chapter. Do each
one as you come to it and then carefully review the explanation that
follows. Moreover, each chapter ends with a practice set. Don’t time
yourself on these practice questions. It’s more important to really
understand how the questions work; you can work on timing later.
When you do these practice sets, don’t just tally up how many you got
right. Rather . . .
Review: Always review the explanation for every practice problem. Think
about why the right answer is right and why the wrong answer is wrong. If
you answered the question incorrectly, think carefully about where your
thinking went astray and use that to inform your next steps. (For example,
in an algebra problem, perhaps you understood the underlying concept
but you made a simple addition error. In that case, the remedy would not
be to study more algebra; rather, the remedy would be to practice adding
and subtracting quickly while avoiding errors.) If you answered the
question correctly, ask yourself whether you got it right for the right
reasons and whether you could have arrived at the same answer more
efficiently.
Repeat this process every time you take a full-length test. Review all the
answers and explanations for every item in the test and think about how
you performed overall.
6. Take full-length practice tests.
Once you have learned, practiced, and reviewed all of the test concepts,
use the full-length tests available in your book and online resources.
Taking a full-length test helps you in four ways:
It reinforces the skills and strategies you’ve learned.
It helps you work on timing.
It gives you a sense of how you’re doing on the various topics and what
you need to work on more.
It helps you learn to cope with test fatigue.
Now, you’ll notice that one item not on that list is “It helps you learn
concepts.” You don’t learn how to approach questions correctly by taking a
full-length test: that learning should be done in an untimed fashion and
accompanied by deep thinking, as described above. That’s why we don’t
recommend that you start your studies by taking a bunch of full-length
tests. However, the last few weeks before Test Day are a perfect time to
take full-length tests.
In addition to the diagnostic test in chapter 2, your Kaplan book has two
full-length practice tests in the back. These follow the ASVAB’s paper-andpencil format. You also have four practice tests in your online resources.
These are computer-based tests that will help you get used to testing using
a computer under the time constraints used by the CAT-ASVAB. While the
computer-based tests in your online account are not adaptive, their
structure does allow you to prepare for the CAT-ASVAB’s format and
content.
MANAGING STRESS
You have a lot riding on the ASVAB. However, you’re also doing the work
you need to do to reach your goals. Unfortunately, though, simply knowing
that you’re working hard won’t make your test anxiety go away. Thus, here
are some stress management tips from our long experience of helping
students prepare for standardized tests.
Clock in and out: Once you’ve set up a study schedule for yourself, treat it
like a job. That is, imagine clocking yourself in and out of ASVAB studies
according to that schedule. Do your best to stick to your schedule, and
when you’re not “clocked in,” don’t let yourself think about the ASVAB.
That will help you release your stress about the test in between study
sessions.
Don’t punish yourself: If you get tired or overwhelmed or discouraged
when studying, don’t respond by pushing yourself harder. Rather, step
away and engage in a relaxing activity like going for a walk, watching a
movie, or playing with your cat or dog. Then, when you’re ready, return to
your studies with fresh eyes.
Breathe: Remember to breathe into your stomach. That forces some of the
muscles that tense up when you’re stressed to relax.
Set small, manageable goals: Each week, set manageable goals related to
your ASVAB progress and reward yourself when you’ve achieved them.
Examples of small goals might be:
This week, memorize and practice the Kaplan Method for Assembling
Objects questions until I no longer have to think about what the steps of
the method are.
This week, try 40 math questions and practice choosing a strategy for
solving each (such as Backsolving, Picking Numbers, estimating,
straight-up math).
This week, review all Paragraph Comprehension question types until I
can identify each question’s type and the appropriate strategy.
Keep yourself healthy: Poor health, fatigue, and isolation make it harder
to cope with stress and anxiety. Get on a regular sleep schedule as much as
possible during your studies, eat well, continue to exercise, and spend time
with those you care about. Also, don’t fuel your studies with caffeine and
sugar. Those substances may make you feel alert, but they can also
damage focus.
Keep the right mindset: Most importantly, keep telling yourself that you
can do this. Don’t fall into the trap of thinking that you’re not “allowed” to
feel confident yet. That’s a self-punishing attitude that will only hurt you.
Rather, remember that confidence breeds success. So let yourself be
confident about your abilities. You’re obviously ambitious and intelligent,
so walk into the ASVAB knowing that about yourself.
If you get discouraged, make a list: If you ever start to wonder if you’ll
ever reach your ASVAB goals, stop what you’re doing and make a list of
everything you’re good at. List every specific skill that you are bringing to
the ASVAB. Examples of specific skills might include:
finding the main point of a paragraph
using suffixes to tell whether a vocabulary word is a noun, verb, or
adjective
identifying what a math question is asking for
factoring a quadratic equation
identifying whether a circuit is built in series or in parallel
identifying types of hammers
Post that list of things you’re good at somewhere you’ll see it every day,
then add to it as you continue to study. We at Kaplan recommend this
because many people focus too heavily on their weaknesses while
preparing for a standardized test. But if you only focus on your
weaknesses, you aren’t seeing an objective picture. There are ASVAB skills
you’re good at. Keep that in mind and focus on building on those
strengths.
FINAL PREPARATIONS FOR TEST
DAY
In the last few weeks before Test Day, do a comprehensive review of all
ASVAB topics. Pay particular attention to the subject tests that are most
important to your preferred career(s) and to the four subject tests that are
most important for enlistment. (Those are Mathematics Knowledge,
Arithmetic Reasoning, Paragraph Comprehension, and Word Knowledge;
see chapter 1 for more information.) Take a full-length test once or twice a
week and use the results of those practice tests to inform your review.
Be sure to contact your recruiter to find out more about what to expect
from Test Day—what you should bring with you, when you can expect your
scores (if you’re taking the paper version of the ASVAB), and other specifics.
IN THE WEEK BEFORE TEST DAY
Your activities in the last week before Test Day should include:
Rest: Make sure you’re on a regular sleep schedule.
Rehearse: Find out where your testing center is located and consider
doing a “dry run.” That is, drive or commute to the testing center around
the same time of day as your testing appointment. You don’t want to be
surprised by traffic or road construction on Test Day.
Review: Do a very brief, high-level review. In other words, flip through the
lessons and rework a few practice problems here and there to reinforce all
of the good habits you’ve developed in your preparation. (Redoing practice
problems you’ve already done is fine: you can actually learn a lot that way
about how to approach those types of questions more efficiently in the
future.)
Stop: Two days before the test, stop studying. No studying at all: you’re not
likely to learn anything new in those two days, and you’ll get a lot more out
of walking into the test feeling rested.
Relax: The evening before the test, do something fun but not crazy or
tiring. Maybe you could have a nice dinner (without alcohol), watch a
movie, or do something else relaxing.
Go to bed at your usual time the night before the exam.
ON TEST DAY ITSELF
On the day of the test, be sure to follow the guidance below:
Warm up: Before you take the test, do an ASVAB warm-up. This can help
your brain get ready to function at its best. You probably can’t take any
practice materials into the testing center, but you can do a few easy
practice problems at home or in the car before you go into the testing
center.
Don’t let nerves derail you: If you feel nervous while taking the test,
remember to breathe deeply into your stomach. Take a few deep breaths
and focus your eyes on something other than the computer screen or test
booklet for a moment.
Keep moving: Don’t let yourself get bogged down on any one question. If
you’re taking the paper version, you can come back to questions that you
weren’t sure about, so skip questions whenever they threaten to slow you
down or to steal time from the other questions. If you’re taking the CATASVAB, you can’t return to previous questions, so you will have to decide to
make a guess whenever a question is threatening to take too much time.
Don’t assess yourself: This is very important. As you’re testing, don’t let
yourself stop and think about how you feel you’re doing. Taking a
standardized test hardly ever feels good. Your own impressions of how it’s
going are totally unreliable. So, instead of focusing on that, remind yourself
that you’re prepared and that you are going to succeed, even if you feel
discouraged as the test is underway.
A er the test, celebrate!
You’ve prepared, practiced, and performed like a champion. Now that the
test is over, it’s time to congratulate yourself on a job well done. Celebrate
responsibly with friends and family, and enjoy the rest of your day,
knowing that you just took an important step toward reaching your goals.
GOOD LUCK!
Everyone at Kaplan wishes you the very best in your studies, on the ASVAB,
and in your military career. We’re rooting for you!
CHAPTER 1
ABOUT THE ASVAB
What Is the ASVAB?
The ASVAB (Armed Services Vocational Aptitude Battery) is the most widely
used multiple-aptitude test battery in the world. It measures a test taker’s
suitability to enlist in the United States Armed Forces and assesses his or
her abilities to be trained in specific civilian or military jobs.
When you take the ASVAB officially, you will be given either a paper-andpencil version of the test or a computer version (also referred to as a
Computer Adaptive Test ASVAB, or CAT-ASVAB). About 70 percent of
prospective recruits take the CAT-ASVAB, so that’s likely to be the version
you’ll encounter.
In this book, you’ll learn how the ASVAB is structured and what it tests.
You’ll also learn strategies and methods that will help you improve your
score significantly in each section.
What Does the ASVAB Test?
In addition to evaluating math and reading skills, the ASVAB
assesses performance in categories such as science, electronics, auto
repair, and the ability to assemble objects. While the section topics and
question types are the same on both the paper-and-pencil and CAT-ASVAB
versions of the test, the amount of time and number of questions will differ
slightly on each version. In the table below, you’ll see the order in which
the ASVAB subtests are arranged, the material tested in each section, and
the differences between the paper-and-pencil and CAT-ASVAB versions.
Additionally, note the sections that are highlighted in gray. These subtests
make up the AFQT, which is discussed in more depth in the following
section. In this table, the subtests are listed in the order in which you’ll take
them on Test Day.
Subtest
Questions
/ Time
Questions
/ Time
Limit in
Minutes
Limit in
Minutes
(CATASVAB)
(Paper &
Pencil)
What’s Tested
Subtest
General Science
(GS)
Questions
/ Time
Questions
/ Time
What’s Tested
Limit in
Minutes
Limit in
Minutes
(CATASVAB)
(Paper &
Pencil)
15
questions
25
questions
Knowledge of general
concepts from life,
/
10
/ 11
minutes
Earth and space, and
physical sciences
minutes
Arithmetic
15
30
Ability to answer word
Reasoning (AR)
questions
questions
problems that involve
/ 42
minutes
/ 36
minutes
basic arithmetic
calculations
Word
Knowledge
15
questions
35
questions
Ability to recognize
synonyms of words
(WK)
/9
minutes
/ 11
minutes
Paragraph
Comprehension
10
questions
15
questions
Ability to answer
questions based on
(PC)
/ 27
minutes
/ 13
minutes
short passages (of 30–
120 words)
Subtest
Questions
Questions
/ Time
/ Time
Limit in
Minutes
(CAT-
Limit in
Minutes
(Paper &
ASVAB)
Pencil)
What’s Tested
Mathematics
15
25
Knowledge of math
Knowledge
questions
questions
concepts, including
(MK)
/ 23
/ 24
arithmetic, algebra,
minutes
minutes
and geometry
Electronics
15
20
Knowledge of
Information (EI)
questions
/
questions
/9
electricity principles
and terminology and of
10
minutes
basic electronic
minutes
circuitry
Auto and Shop
10
25
Knowledge of
Information
questions
questions
automobiles and of
(AS)*
/7
/ 11
tool and shop practices
minutes
and
minutes
and terminology
10
questions
/6
minutes
Subtest
Questions
/ Time
Questions
/ Time
Limit in
Limit in
Minutes
Minutes
(CAT-
(Paper &
ASVAB)
Pencil)
What’s Tested
Mechanical
15
25
Knowledge of basic
Comprehension
(MC)
questions
/ 22
questions
/ 19
mechanical and
physical principles
minutes
minutes
Assembling
15
25
Ability to determine
Objects (AO)
questions
questions
how a disassembled
/ 17
/ 15
object will look when it
minutes
minutes
is put back together
135
225
questions
questions
/ 173
minutes
/ 149
minutes
Totals
*On the CAT-ASVAB, Auto and Shop Information is split into two parts (Auto
Information [AI] and Shop Information
[SI]), but one score is reported.
What Is the AFQT?
While the ASVAB is designed to determine a potential recruit’s
occupational fit in the military, there is no actual “overall” ASVAB score.
When people talk about getting a score of, say, a 75 or 80 on the ASVAB,
they are really talking about something called the AFQT (Armed Forces
Qualification Test) score. A candidate’s score on the AFQT determines that
candidate’s eligibility for all branches of the Armed Services. The AFQT
score is derived from your performance on just the verbal and math
subtests of the ASVAB, as explained below.
Your AFQT Score
The military determines your AFQT score by first adding your Word
Knowledge and Paragraph Comprehension scores together to get your
Verbal Expression or VE score. The formula to derive the AFQT raw score is
2VE + AR (Arithmetic Reasoning) + MK (Mathematics Knowledge) = AFQT
score.
2 × [Word Knowledge + Paragraph Comprehension]
+
[Arithmetic Reasoning + Mathematics Knowledge]
= AFQT RAW SCORE
The AFQT raw score you receive is then translated into a percentile score
that tells you how well you did on the AFQT compared to a base group of
approximately 6,000 other test takers ages 18–23. For instance, if your
percentile score is 68, you scored as well as or better than 68 percent of the
base group. This AFQT percentile score is used to determine your eligibility
for the armed forces.
AFQT Qualifying Scores for Different
Branches of the Military
The requirements listed below are minimum standards for high school
graduates and are subject to change. The scores necessary for many
occupations and for enlistment bonuses are usually significantly higher.
Also, these are the requirements for high school graduates; the
requirements are more stringent for those who have earned their high
school equivalency diplomas by taking the GED® test, the TASC test, or the
HiSET® exam. An applicant without a high school degree or equivalent can
be accepted into military service only in special circumstances.
Applicants who possess special skills or experience (for example, fluency in
a certain language or computer programming experience) may be eligible
for waivers of AFQT minimum scores. Also, if you score well on any
subtest(s) that relate to particular occupations that are recruiting targets,
you may be able to get a waiver.
You should refer to the services’ websites or publications for more specific
information or contact a military recruiter.
Air Force—minimum AFQT score of 31
Army—minimum AFQT score of 31
Marine Corps—minimum AFQT score of 31
Navy—minimum AFQT score of 35
Coast Guard—minimum AFQT score of 40
ASVAB Logistics
Registering for and Taking the ASVAB
Unless you are taking the ASVAB at your high school as part of the
Department of Defense Career Exploration Program, your first step toward
registering to take the ASVAB is to contact the local recruiter for the service
branch that you wish to join. The recruiter will help you complete your
enlistment application; you will need to provide necessary documentation.
Once you have met the basic qualifications for enlistment, the recruiter will
schedule either a proctored ASVAB test or an unproctored form of the
ASVAB called the PiCAT.
The Pending Internet Computerized Adaptive Test (PiCAT) is an
unproctored, full-length ASVAB that you take on your own time. Your local
recruiter will get you registered and give you an access code. Your recruiter
can also tell you your score a er you've finished the test. Then, if you
choose to enlist, you'll take a proctored verification test that is much
shorter than the ASVAB, only 25–30 minutes, to confirm your PiCAT score.
The Armed Forces have been piloting another potential military entrance
assessment, the Tailored Adaptive Personality Assessment System
(TAPAS). Based on the studies conducted so far, this computer-adaptive
personality test is thought to provide information about recruits'
motivation and other noncognitive characteristics that indicate whether
they will be successful a er enlistment. The TAPAS consists of 120
questions and, as of this writing, continues to be offered to certain
candidates who also take the ASVAB as a way of continuing to evaluate the
test's usefulness. The military's goal is to use the additional information
provided by the TAPAS to identify recruits who will perform well, despite
not quite meeting threshold AFQT scores.
ASVAB results are valid for two years. A er taking an initial ASVAB test, you
may retake it a er one calendar month. A er the first retest, you may take
another retest a er another calendar month has passed. If you have had
two retests, you must wait at least six months before taking the test again.
How to Read Your ASVAB Scores
Your official ASVAB scores will come in a variety of styles and will be fully
explained to you by your guidance counselor or recruiter. All of the scores
matter, though some may matter more than others. Here’s a quick
breakdown of what you will find.
AFQT Score—You will receive a single numerical score for the AFQT.
Standard Scores—You will receive a Standard Score for each of the
subtests. These scores are calculated using a comparison of your raw
scores to the raw scores of a standard national sample. According to the
Department of Defense, roughly half the population achieves a Standard
Score of 50 or above but only about 16 percent scores higher than 59.
Service Composite Scores—These score combinations, sometimes called
Line Scores, are used to determine whether a test taker has the necessary
vocational aptitude to be trained for different job assignments in all the
military branches. For example, a Navy Engineering Aid composite score
(abbreviated EA) is the sum of twice the Mathematics Knowledge score
plus the Arithmetic Reasoning and General Science scores. An enlistee
must achieve a minimum composite score for the vocation of interest to be
able to qualify to be trained for the job. To cite another example, to qualify
for electronics training and occupations in the Army, you must attain a
certain score that combines your results on the General Science, Arithmetic
Reasoning, Mathematics Knowledge, and Electronics Information tests. For
more detailed information, contact your local recruiter or visit the website
for your service branch of interest.
Career Exploration Scores—In addition to the Standard Scores, students
who take the ASVAB in their high schools as part of the Career Exploration
Program receive three Career Exploration Scores in the composite areas of
Verbal Skills, Math Skills, and Science and Technical Skills, which are all
reported as standard scores and as percentiles relative to grade in school
and gender.
Different Versions of the ASVAB
Depending upon your reasons for taking the ASVAB and your stage in the
career decision-making process, you will take on one of the following three
versions of the test battery:
Enlistment Testing Program ASVAB
This version of the ASVAB, sometimes referred to as the Production Version,
is used for enlistment purposes only and is administered to potential
enlistees in all branches of the military. A potential recruit’s performance
on the ASVAB subtests is used to determine whether the candidate has the
necessary aptitudes to enlist in a desired branch of service and for which
military jobs the candidate is best suited.
Career Exploration Program ASVAB
This version of the ASVAB is administered, along with an interest inventory,
to high school and postsecondary students as part of the Department of
Defense’s Career Exploration Program. The content and format of this
ASVAB are the same as the enlistment version, with one exception: in the
paper-and-pencil version, the Assembling Objects subtest is not given.
Armed Forces Classification Test (AFCT)
Also known as the “In-Service” ASVAB, the AFCT is administered to those
already in the military who are looking to switch jobs within the military. It
is identical to the paper-and-pencil version of the ASVAB given prior to
enlistment.
The Paper-and-Pencil Test vs. the CAT
Computer-adaptive testing, or CAT for short, is just a fancy way of saying
that the difficulty of the questions you get on the test adapts based on your
performance up to that point.
The diagram below models how a computer-adaptive test works. In the
diagram, each dot represents a question. Each question is labeled with
whether the test taker got the question correct (C) or incorrect (I). The
graph also shows the difficulty of each question.
The first question you will see will be of medium difficulty—that is, it will be
aligned to the average ability of test takers. Notice that each time you
answer a question correctly, you “earn” a more difficult question, which is
aligned to a higher scoring level. Each time you give an incorrect answer,
your next question will be easier and thus aligned to a lower scoring level.
The CAT continues to adapt until you are getting roughly half of the
questions you see correct. Once your performance has stabilized in this
way, the CAT determines your score based on the difficulty level around
which your answers are hovering.
Some test takers think they can get a high score by working slowly, making
sure to get questions right and driving up their score, even if that means
they run out of time before answering all the questions. However, the
makers of the ASVAB have thought of this, and the scoring includes a
penalty for every question le unanswered, eliminating any advantage
that might be gained. Therefore, it's important to stay on pace so you finish
each section with enough time to do your best on the last question, even if
that means guessing on some questions along the way.
Studies have shown that, overall, people perform the same on the ASVAB
whether they take the paper or CAT version of the test. There are, however,
some individuals who will tend to do better on one version of the test than
the other. Now, you may not have a choice regarding which version of the
ASVAB you take. If you do have a choice, here are some of the advantages
and disadvantages of taking the CAT versus the paper test:
Advantages of Taking the CAT-ASVAB
You need to answer far fewer questions than on the paper-and-pencil
ASVAB, and you get more time per question to answer.
The test can be scored immediately. You will know how well you did as
soon as you finish the test.
The test administration is very flexible, so you don’t have to wait for the
next scheduled test date to take the test.
There’s no chance of losing points by filling out your answer sheet
incorrectly.
The CAT format gives you the chance to work methodically on one
question at a time with no other questions there to distract you.
Disadvantages of Taking the CAT-ASVAB
You cannot skip around on this test; you must answer the questions one
at a time in the order the computer gives them to you.
If you realize later that you answered a question incorrectly, you cannot
go back and change your answer.
You can’t cross off an answer choice, so you’ll have to use your scrap
paper to keep track of the answers you’ve eliminated.
Kaplan’s ASVAB Strategies
Always answer every question—There is no guessing penalty on the
ASVAB. This means that it is absolutely in your interest to guess on every
question on every subtest of the ASVAB! Even if you have to make a
completely random guess, you have a 25 percent chance of picking the
correct answer. Remember, too, that on the CAT-ASVAB, unanswered
questions at the end of a section result in a penalty to your score, so you
definitely want to get to every question.
Familiarize yourself with the test—One key to success on the ASVAB is
knowing what to expect. The format—which includes the directions, the
types of questions, and even the traps that the test maker places among
the answer choices—is remarkably similar from test to test. One of the
easiest things you can do to improve your performance on the ASVAB is to
understand the test format before you take the test.
Practice, practice, practice—Completing this book's practice sets and fulllength tests, as well as using the Qbank, will help you improve your scores
for three reasons. First, it will help you brush up on topics that you may not
have seen for a while. Second, practice improves your speed. Third, as
mentioned above, practicing will help you recognize patterns and trap
answers.
Take advantage of the multiple-choice format—You start with a 25
percent chance of getting the correct answer by random guessing, but
eliminating any of the answer choices improves your odds. If you know
that one of the four choices cannot be right and eliminate it accordingly,
you now have a 33 percent chance of getting the correct answer. Remove
one more wrong answer choice, and your chance of getting the question
right is now 50–50. On certain ASVAB questions, you will find that
eliminating wrong choices is as effective as spotting the correct answer the
straightforward way. O en, even if you are completely confused by a
question, you can still make a solid guess by eliminating answer choices
that run counter to the other three choices.
CAT-ASVAB Strategies
If you are taking the CAT-ASVAB, applying certain CAT-specific strategies
will have a direct, positive impact on your score:
Work at the same steady pace throughout each section. Questions
earlier in the section tend to affect your score more than later questions.
However, if you spend extra time getting these questions right, you’ll
begin to get much harder questions and you’ll have less time to do
them. This will result in missing a string of questions and maybe even
leaving some questions unanswered, undoing all of your early gains.
As you progress through the middle part of a section, try to avoid getting
several questions in a row wrong, as this can sink your score. If you
know that you answered the previous question with a random guess,
spend a little extra time trying to get the next one right.
The CAT does not allow you to skip questions. So if you are given a
question you cannot answer, you’ll have to guess. Guess strategically by
eliminating any choices that you know are wrong and choosing from
those remaining. Once you know you'll need to guess, do so quickly and
move on; if you don't know the answer, staring at the question longer is
unlikely to produce enlightenment.
Don’t get rattled if you see difficult questions. Because the CAT increases
in difficulty when you get correct answers, earning difficult questions
just means that you are doing well. Moreover, keep in mind that the CAT
will continue to adapt until you are answering roughly half of the
questions you see correctly. Thus, toward the end of the test, you likely
will feel that you are getting about half the questions you see wrong.
That means the test is working the way it should. So don’t get
discouraged—just keep doing your best and keep your confidence up!
Getting Ready for the ASVAB
This book is divided into chapters that offer specific test-taking strategies
for dealing with each of the subtests, with emphasis on those subtests that
constitute the AFQT. Your online resources are organized in the same way
as the book. Kaplan recommends that you take the first practice test, in
chapter 2, before you work through this book and the online videos and
Qbank. By doing so, you can pay special attention to the areas that were
difficult for you as you progress through the book. You’ve made the right
move in deciding to prepare for the ASVAB. It is a highly coachable test,
and we will give you the tools you need to score high on the ASVAB and
qualify for the military career you desire.
CHAPTER 2
ASVAB DIAGNOSTIC TEST
About The Diagnostic Test
This diagnostic test is intended to help guide you in your ASVAB
preparation. You’ll learn several things at once by taking this diagnostic
test:
What’s on the ASVAB: This diagnostic test will help you become familiar
with the topics and question types that will appear on the ASVAB. A er
taking the diagnostic test, review your answers carefully, and make mental
notes about the question types or topics that seem least familiar.
What your strengths and areas of opportunity are: The diagnostic
mimics the paper-and-pencil ASVAB, rather than the CAT-ASVAB, which
means it has more questions than you’ll see on the CAT-ASVAB. There’s a
good reason for that: the greater number of questions on this diagnostic
test will allow you to see more clearly which topics you need more work
on.
How you react to test fatigue: Find a quiet space where you won’t be
interrupted for about three hours. Take this test under timed conditions,
one subject a er another in the order they appear here. You can take a five-
minute bathroom break if needed, but don’t let yourself take a long break.
This experience will help you assess how ready you are to focus on test
material for an extended time period. If you find that fatigue interferes with
your performance, be sure to take a full-length test (either in the book or
online) each week in the last few weeks before your test date.
Hint: If you run out of time before you finish any given section, be sure to
fill in all the blanks on your answer sheet, as there’s no wrong answer
penalty and some of your guesses could turn out to be correct! Good luck!
Answer Sheet
On Test Day you will see an Answer Sheet like below.
ASVAB DIAGNOSTIC TEST
Part 1: General Science (GS)
11 Minutes
— 25
Questions
Directions: In this section, you will be tested on your knowledge of
concepts in science generally reviewed in high school. For each
question, select the best answer and mark the corresponding oval
on your answer sheet.
1.
are necessary for the body’s maintenance, growth, and
repair.
(A) Proteins
(B) Carbohydrates
(C) Fats
(D) Vitamins
2. On a Fahrenheit thermometer, the boiling point of water at sea
level is
(A) 100°
(B) 180°
(C) 212°
(D) 373°
3. The process by which the body’s cells use oxygen and glucose to
produce energy, while releasing carbon dioxide and water vapor as
waste products, is known as
(A) decomposition
(B) photosynthesis
(C) oxidation
(D) respiration
4.
carry blood back to the heart from the capillaries.
(A) Arteries
(B) Veins
(C) Ventricles
(D) Red blood cells
5. Which of the following is an example of a chemical process?
(A) Helium mixes with neon.
(B) Iron forms rust.
(C) Sugar dissolves in water.
(D) Ice melts.
6. A universal donor is a person with which of the following blood
types?
(A) O negative
(B) A positive
(C) AB positive
(D) B negative
7. Blood enters the right atrium of the heart from the
(A) aorta
(B) le ventricle
(C) pulmonary vein
(D) vena cava
8. Which of the following substances has the highest pH?
(A) ammonia
(B) battery acid
(C) isopropyl alcohol
(D) water
9. Which of the following organs does the most work to break down
food using enzymes?
(A) pancreas
(B) stomach
(C) small intestine
(D) large intestine
10. Which of the following is NOT part of the female reproductive
system?
(A) oviduct
(B) uterus
(C) ovary
(D) testes
11. The most basic unit of inheritance is known as a
(A) phenotype
(B) genotype
(C) chromosome
(D) gene
12. Which of the following is a sedimentary rock?
(A) granite
(B) marble
(C) shale
(D) slate
13. A producer is also known as a(n)
(A) heterotroph
(B) saprotroph
(C) autotroph
(D) scavenger
14. A vulture would be considered a
(A) producer
(B) decomposer
(C) scavenger
(D) parasite
15. What type of rock is obsidian?
(A) sedimentary
(B) igneous
(C) metamorphic
(D) sandstone
16. During a lunar eclipse
(A) the Moon lies between the Earth and Sun
(B) the Sun lies between the Moon and Earth
(C) the Earth lies between the Moon and Sun
(D) the Sun lies outside the Moon’s umbra
17. A centimeter is
(A) one hundredth of a meter
(B) one tenth of a meter
(C) ten meters
(D) one hundred meters
18. Momentum is
(A) the push or pull that forces an object to change its speed or
direction
(B) the rate of change of velocity
(C) the rate at which an object changes position
(D) the tendency of an object to continue moving in the same
direction
19. Which color’s light waves have the highest frequency?
(A) yellow
(B) green
(C) red
(D) violet
20. The major portion of an atom’s mass consists of
(A) neutrons and protons
(B) electrons and protons
(C) electrons and neutrons
(D) neutrons and positrons
21. Which of the following is NOT an example of an arthropod?
(A) crab
(B) centipede
(C) sea urchin
(D) spider
22. Table salt is considered a(n)
(A) ionic compound
(B) semi-ionic compound
(C) covalent compound
(D) element
23. Over the course of 24 hours
(A) the Earth rotates 360° around the sun
(B) the Moon rotates 360° around the Earth
(C) the Earth rotates 360° about its axis
(D) the Moon rotates 360° about its axis
24. Which of the following kingdoms is composed of prokaryotic life
forms such as bacteria, and as such is considered the most
primitive?
(A) Fungi
(B) Protista
(C) Monera
(D) Plantae
25. Human beings belong to the phylum
(A) Animalia
(B) Chordata
(C) Mammalia
(D) Primata
IF YOU FINISH BEFORE THE TIME IS UP, YOU MAY CHECK
OVER YOUR WORK ON THIS PART ONLY.
STOP
ASVAB DIAGNOSTIC TEST
Part 2: Arithmetic Reasoning (AR)
36
Minutes
— 30
Questions
Directions: In this section, you are tested on your ability to use
arithmetic. For each question, select the best answer and mark the
corresponding oval on your answer sheet.
1. John bought a camera on sale that normally costs $160. If the price
was reduced 20% during the sale, what was the sale price of the
camera?
(A) $120
(B) $124
(C) $128
(D) $140
2. A subway car passes 3 stations every 10 minutes. At this rate, how
many stations will it pass in one hour?
(A) 15
(B) 18
(C) 20
(D) 30
3. On a certain map,
inch represents one mile. What distance, in miles, is
represented by
inches?
(A)
(B)
(C)
(D)
4. A certain box contains baseballs and golf balls. If the ratio of
baseballs to golf balls is 2:3 and there are 30 baseballs in the box,
how many golf balls are in the box?
(A) 18
(B) 20
(C) 36
(D) 45
5. Four people shared a taxi to the airport. The fare was $36.00, and
they gave the driver a tip equal to 25% of the fare. If they equally
shared the cost of the fare and tip, how much did each person pay?
(A) $9.75
(B) $10.25
(C) $10.75
(D) $11.25
6. If a car travels
of a kilometer each second, how many kilometers does it
travel in an hour?
(A) 36
(B) 60
(C) 72
(D) 100
7. 20 − (-5) =
(A) -25
(B) 25
(C) 15
(D) -15
8. Ms. Smith drove a total of 700 miles on a business trip. If her car
averaged 35 miles per gallon of gasoline and gasoline cost $1.25 per
gallon, what was the cost in dollars of the gasoline for the trip?
(A) $20.00
(B) $24.00
(C) $25.00
(D) $40.00
9. A er eating 25% of the jelly beans, Brett had 72 le . How many jelly
beans did Brett have originally?
(A) 90
(B) 94
(C) 95
(D) 96
10. A student finishes the first half of an exam in the time it takes him to
finish the second half. If the entire exam takes him an hour, how
many minutes does he spend on the first half of the exam?
(A) 20
(B) 24
(C) 27
(D) 36
11. A 25-ounce solution is 20% alcohol. If 50 ounces of water are added
to it, what percent of the new solution is alcohol?
(A)
(B)
(C) 10%
(D)
12. Marty has exactly 5 blue pens, 6 black pens, and 4 red pens in his
backpack. If he pulls out one pen at random from his backpack,
what is the probability that the pen is either red or black?
(A)
(B)
(C)
(D)
13. From 1980 through 1990, the population of Country X increased by
100%. From 1990 to 2000, the population increased by 50%. What
was the combined increase for the period 1980–2000?
(A) 150%
(B)
(C) 175%
(D) 200%
14. If a
worker earns $200 for
the first 40 hours of work in a week and then is paid one-and-onehalf times
her regular rate for any additional hours, how many hours must
she work to make $230 in a week?
(A) 43
(B) 44
(C) 45
(D) 46
15. If 50% of x is 150, what is 75% of x?
(A) 225
(B) 250
(C) 275
(D) 300
16. The total fare for two adults and three children on an excursion
boat is $14. If each child’s fare is one half of each adult’s fare, what
is the adult fare?
(A) $2.00
(B) $3.00
(C) $3.50
(D) $4.00
17. What is the prime factorization of 140?
(A) 2 × 70
(B) 2 × 3 × 5 × 7
(C) 2 × 2 × 5 × 7
(D) 2 × 2 × 2 × 5 × 7
18. A painter charges $12 an hour while his son charges $6 an hour. If
the father and son worked the same amount of time together on a
job, how many hours did each of them work if their combined
charge for their labor was $108?
(A) 6
(B) 9
(C) 12
(D) 18
19. 4! =
(A) 4
(B) 16
(C) 24
(D) 256
20. At garage A, it costs $8.75 to park a car for the first hour and $1.25
for each additional hour. At garage B, it costs $5.50 to park a car for
the first hour and $2.50 for each additional hour. What is the
difference between the cost of parking a car for 5 hours at garage A
and parking it for the same length of time at garage B?
(A) $2.25
(B) $1.75
(C) $1.50
(D) $1.25
21. Jan types at an average rate of 12 pages per hour. At that rate, how
long will it take Jan to type 100 pages?
(A) 8 hours and 10 minutes
(B) 8 hours and 15 minutes
(C) 8 hours and 20 minutes
(D) 8 hours and 30 minutes
22. Two large sodas contain the same amount as three medium sodas.
Two medium sodas contain the same amount as three small sodas.
How many small sodas contain the same amount as eight large
sodas?
(A) 24
(B) 18
(C) 16
(D) 12
23. If each digit 5 in the number 258,546 is replaced with the digit 7, by
how much will the number be increased?
(A) 2,020
(B) 2,200
(C) 20,020
(D) 20,200
24. Michael bought
pounds of lumber at $4.00 per pound. If a 7% sales tax was
added, how much did Michael pay?
(A) $9.63
(B) $9.98
(C) $10.70
(D) $11.77
25. The ratio of
to
is equivalent to the ratio of
(A) 3 to 5
(B) 4 to 7
(C) 8 to 13
(D) 13 to 21
26. A cat is fed
of a pound of cat food every day. For how many days will 72
pounds of this cat food feed the cat?
(A) 160
(B) 172
(C) 180
(D) 192
27. A er spending
of
her salary,
Eva has $420 le . What is
her salary?
(A)
(B)
(C)
(D)
$175
$245
$720
$1,008
28. A stock decreases in value by 20%. By what percent must the stock
price increase to reach its former value?
(A) 15%
(B) 20%
(C) 25%
(D) 40%
29. Joan can shovel a certain driveway in 50 minutes. If Mary can
shovel the same driveway in 20 minutes, how long will it take them,
to the nearest minute, to shovel the driveway if they work together?
(A) 12
(B) 13
(C) 14
(D) 15
30. June’s weekly salary is $70 less than Kelly’s, which is $50 more than
Eileen’s. If Eileen earns $280 per week, how much does June earn
per week?
(A) $160
(B) $260
(C) $280
(D) $300
IF YOU FINISH BEFORE THE TIME IS UP, YOU MAY CHECK
OVER YOUR WORK ON THIS PART ONLY.
STOP
ASVAB DIAGNOSTIC TEST
Part 3: Word Knowledge (WK)
11
Minutes
— 35
Questions
Directions: In this section, you are tested on the meaning of words.
Each of the following questions has an underlined word. Select the
answer that most nearly means the same as the underlined word
and mark the corresponding oval on your answer sheet.
1. Noble most nearly means
(A) comely
(B) loose
(C) aristocratic
(D) lackadaisical
2. John initially disagreed with Megan, but then he had to concede
her point about the budget.
(A) argue
(B) understand
(C) counter
(D) admit
3. Goad most nearly means
(A) listen
(B) provoke
(C) pacify
(D) ignore
4. Teenagers at the mall love to roam in a herd.
(A) jacket
(B) line
(C) pack
(D) ratio
5. Panicking in an emergency is not a viable response for an EMT.
(A) total
(B) collective
(C) lucid
(D) workable
6. Judicious most nearly means
(A) accessible
(B) cold
(C) wise
(D) talkative
7. Hesitating in a time of crisis can o en lead to failure.
(A) broadening
(B) creating
(C) leaving
(D) pausing
8. Applicants who insist on falsifying information ruin the process for
everyone.
(A) fabricating
(B) listing
(C) furthering
(D) taking on
9. Hollow most nearly means
(A) dangerous
(B) potent
(C) empty
(D) superb
10. Coax most nearly means
(A) advise
(B) trade
(C) plead
(D) grace
11. The monotonous speech le them all feeling sleepy.
(A) telling
(B) boring
(C) caustic
(D) hilarious
12. As Mrs. Higgins attempted to teach the difficult material, she
sensed growing consternation among her students.
(A) desires
(B) inability
(C) frustration
(D) behavior
13. With the holidays approaching, Dave looked forward to a savory
feast or two.
(A) tasty
(B) guilty
(C) heroic
(D) skimpy
14. A man of some renown, the mayor walked with his chest puffed
out.
(A) size
(B) fame
(C) confusion
(D) toil
15. Raconteur most nearly means
(A) believer
(B) storyteller
(C) standout
(D) pedant
16. She felt that nothing could really quench her curiosity.
(A) justify
(B) break
(C) illuminate
(D) satisfy
17. The committee was polarized on the issue.
(A) split
(B) disgusted
(C) grateful
(D) cold
18. The need to be precise was clear to everyone.
(A) a er the fact
(B) cautious
(C) exact
(D) barren
19. Drucker surveyed the terrain before him for water.
(A) oversight
(B) landscape
(C) river
(D) goal
20. Terminal most nearly means
(A) easy
(B) glittering
(C) busy
(D) final
21. Augment most nearly means
(A) cra
(B) end
(C) throw away
(D) enhance
22. Her involuntary spasm knocked over a lamp.
(A) unintentional
(B) painful
(C) listless
(D) binary
23. The other owners accused the brothers of collusion.
(A) coalition
(B) secret agreement
(C) hoping
(D) pretending
24. The mongoose shows great tenacity in the face of danger.
(A) fear
(B) candor
(C) determination
(D) speed
25. Tactile most nearly means
(A) ghastly
(B) easy
(C) patient
(D) tangible
26. The dark clouds seemed to portend a gloomy weekend ahead.
(A) fake
(B) lose
(C) predict
(D) edit
27. Germinate most nearly means
(A) sprout
(B) oppress
(C) adulate
(D) foster
28. Restore most nearly means
(A) trip up
(B) invigorate
(C) care for
(D) toughen
29. Filament most nearly means
(A) horse
(B) triage
(C) nightmare
(D) thread
30. Whatever the original intent, the focus has clearly mutated at this
point.
(A) disappeared
(B) reiterated
(C) altered
(D) intensified
31. To be elected president, one must be a calm yet still dynamic
figure.
(A) reassuring
(B) exciting
(C) manic
(D) terrible
32. Congeal most nearly means
(A) fade
(B) swirl
(C) harden
(D) undulate
33. Reconnoiter most nearly means
(A) advance
(B) posit
(C) grade
(D) scout
34. Whether one can accrue enough money to live on is always the
question.
(A) accumulate
(B) acquiesce
(C) trap
(D) magnify
35. His innate ability to make the correct turn was amazing.
(A) unsure
(B) discussed
(C) creative
(D) natural
IF YOU FINISH BEFORE THE TIME IS UP, YOU MAY CHECK
OVER YOUR WORK ON THIS PART ONLY.
STOP
ASVAB DIAGNOSTIC TEST
Part 4: Paragraph Comprehension
(PC)
13
Minutes
— 15
Questions
Directions: This section contains paragraphs followed by
incomplete statements or questions. For each question, read the
paragraph and select the answer that best completes the
statements or answers the question that follows. Mark the
corresponding oval on your answer sheet.
1. The first detective stories, written by Edgar Allan Poe and Arthur
Conan Doyle, emerged in the mid-nineteenth century, at a time
when there was enormous public interest in science. The
newspapers of the day continually publicized the latest scientific
discoveries, and scientists were acclaimed as the heroes of the age.
Poe and Conan Doyle shared this fascination with the methodical,
logical approach used by scientists in their experiments, and
instilled their detective heroes with outstanding powers of
scientific reasoning.
The main idea of this passage is
(A) science fiction was not popular among nineteenth-century
readers
(B) scientific progress made its way into the fiction of the time
(C) newspapers detailed detective work each day
(D) the first detective stories were written by scientists
2. Children have an amazing talent for learning vocabulary. Between
the ages of one and seventeen, the average child learns the
meaning of about 80,000 words—about 14 per day. Dictionaries
and traditional classroom vocabulary lessons only account for part
of this knowledge growth. More important are individuals’ reading
habits and their dialogues with people whose vocabularies are
larger than their own. Reading shows students how words are used
in sentences. Conversation offers students the chance to ask
questions about the language.
According to the passage, reading is valuable to students because
(A) children learn differently than adults
(B) words used in stories are generally harder
(C) reading provides vocabulary clues within sentences
(D) vocabulary is learned mostly through conversation
3. The first truly American art movement was formed by a group of
landscape painters that emerged in the early nineteenth century
called the Hudson River School. The first works in this style were
created by Thomas Cole, Thomas Doughty, and Asher Durand, a
trio of painters who worked during the 1820s in the Hudson River
Valley and surrounding locations. Heavily influenced by European
artists, these painters set out to convey the remoteness and
splendor of the American wilderness. The strongly patriotic tone of
their paintings caught the spirit of the times, and within a
generation the movement had grown to include landscape painters
from all over the United States.
The passage is primarily concerned with which of the following?
(A) the history of the Hudson River School of painters
(B) American art movements of the nineteenth century
(C) how American landscape painters were influenced by
European painters
(D) the artistic origins of nationalism in the United States
4. Different people have different approaches to choosing a personal
computer. Some people pick a new computer at random, falling
victim to the latest trend or advertisement. These people o en
regret their decisions in the long run. On the other hand, people
who do thorough research before purchasing a computer are much
happier with their decisions in the long run. When you are shopping
for a new computer, conducting research is an important step.
Which of the following statements best expresses the main idea of
the passage?
(A) People should base computer purchase decisions on
advertisements.
(B) People should not base computer purchase decisions on
advertisements.
(C) People should conduct research to be happy in life.
(D) People should conduct research before purchasing a
computer.
Questions 5 and 6 refer to the following passage.
The painter Georgia O’Keeffe was born in Wisconsin in 1887 and grew up
on her family’s farm. At seventeen she decided she wanted to be an artist
and le the farm for schools in Chicago and New York, but she never lost
her bond with the land. Like most painters, O’Keeffe painted the things
that were most important to her, and nearly all her works are portrayals of
nature. O’Keeffe became famous when her paintings were discovered in
New York by the photographer Alfred Stieglitz, whom she married in 1924.
During a visit to New Mexico in 1929, O’Keeffe was so moved by the bleak
landscape and broad skies of the Western desert that she began to paint its
images.
5. In this context, the word bleak most nearly means
(A) empty
(B) moody
(C) cold
(D) vivid
6. Georgia O’Keeffe’s work generally shows
(A) an ability to paint something complex accurately
(B) her love for Alfred Stieglitz
(C) her desire for fame
(D) her love of the land
7. The four brightest moons of Jupiter were the first objects in the
solar system discovered with the use of the telescope. This proof
played a central role in Galileo’s famous argument in support of the
Copernican model of the solar system, in which the planets are
described as revolving around the Sun. For several hundred years,
scientific understanding of these moons was slow to develop. But
spectacular close-up photographs sent back by the 1979 Voyager
missions forever changed our perception of these moons.
Which best describes the Copernican model of the solar system?
(A) Planets move counterclockwise as they rotate.
(B) The Sun and other planets revolve around the Earth.
(C) The planets move in orbit around the Sun.
(D) The four brightest moons of Jupiter used to be planets.
8. As the sky opened up and sun at last rushed into the room, Toby
smiled knowing that the game would proceed as planned. It had to,
if only because his father would be there and it might be the last
opportunity he would have to see Toby play. Now the birds began
to appear here and there. Toby got out his baseball glove and ball
and waited for his dad to arrive to take him to the game.
The mood of the character in the passage is
(A) sad
(B) careless
(C) uneasy
(D) eager
9. A human body can survive without water for several days and
without food for as many as several weeks. If breathing stops for as
little as three to six minutes, however, death is likely. All animals
require a constant supply of oxygen to the body tissues, and
especially to the heart or brain. In the human body, the respiratory
and circulatory systems perform this function by delivering oxygen
to the blood, which then transports it to tissues throughout the
body. Respiration in large animals involves more than just
breathing in oxygen. It is a complex process that delivers oxygen
while eliminating carbon dioxide produced by cells.
Which bodily function, according to the passage, is least essential
to the immediate survival of a human being?
(A) eating
(B) drinking
(C) breathing
(D) excretion
10. The media are really out of control. When the press gets a story, it
seems that within minutes it has produced flashy moving graphics
and sound effects to entice viewers and garner ratings. Real facts
and unbiased coverage of an issue are totally abandoned in
exchange for an overly sentimental or one-sided story that too
o en distorts the truth. Viewers need to learn to distinguish real
reporting from the junk on nearly every television channel these
days.
The author would be most likely to agree with which of the
following?
(A) Newspapers should have more editorials.
(B) Flashy graphics add substance to television news reporting.
(C) Objective news reporting is a dying art.
(D) Television news anchors are valuable sources of information.
11. The poems of the earliest Greeks, like those of other ancient
societies, consisted of magical charms, mysterious predictions,
prayers, and traditional songs of work and war. These poems were
intended to be sung or recited, not written down, since they were
created before the Greeks began to use writing for literary
purposes. The different forms of early Greek poetry all had
something in common: they described the way of life of the Greek
people. Poetry expressed ideas and feelings that were shared by
everyone in a community—their folktales, their memories of
historical events, and their religious speculation.
Early Greek poetry was which of the following?
(A) mainly an oral form
(B) a departure from poetic traditions in other societies
(C) widely thought to be an act of the gods
(D) usually about lost love and sadness
12. In computer design, the effectiveness of a program generally
depends on the ability of the programmer. Still, remarkable
progress has been made in the development of artificial
intelligence. This progress has scientists wondering whether it will
eventually be possible to develop a computer capable of intelligent
thought. When a computer defeated Garry Kasparov, considered by
many the greatest chess player of all time, it was taken to be a
vindication of the claims of the strongest supporters of artificial
intelligence. Despite this accomplishment, others argue that while
computers may imitate the human mind, they will never possess
the capacity for true intelligence.
The main idea of this passage is
(A) computers can never learn to think
(B) chess is a game in which computers are superior
(C) great strides have been made in artificial intelligence
(D) artificial intelligence is a scientific miracle
Questions 13 and 14 refer to the following passage.
Coral reefs are created over the course of hundreds or even thousands of
years. The main architect in coral reef formation is the stony coral, a
relative of the sea anemone that lives in tropical climates and secretes a
skeleton of almost pure calcium carbonate. Its partner is the green alga, a
tiny unicellular plant that lives within the tissues of the coral. The two
organisms form a mutually beneficial relationship, with the algae
consuming carbon dioxide given off by the corals, and the corals thriving
on the abundant oxygen produced photosynthetically by the algae. When
the coral dies, its skeleton is le , and other organisms grow on top of it.
Over the years, the mass of coral skeletons together with those of
associated organisms combine to form the petrified underwater forest that
divers find so fascinating.
13. Which of the following best describes what this passage is about?
(A) the varieties of animal life that live in coral reefs
(B) the formation of coral reefs
(C) the life and death cycles of coral reefs
(D) the physical beauty of coral reefs
14. The relationship between the coral and the algae is best described
as
(A) parasitic
(B) competitive
(C) predatory
(D) cooperative
15. For do-it-yourself types, the cost of getting regular oil changes
seems unnecessary. A er all, the steps are fairly easy as long as you
are safe. First, make sure that the car is stationary and on a level
surface. Always use the emergency brake to ensure that the car
does not roll on top of you. Next, locate the drain plug for the oil
under the engine. Remember to place the oil drain pan under the
plug before you start. When it is drained fully, wipe off the drain
plug and the plug opening and then replace the drain plug. Next,
simply place your funnel in the engine and pour in new oil. Be sure
to return the oil cap when you’re done. Finally, run the engine for a
minute, and then check the dipstick to see if you need more oil in
your engine.
A er draining the old oil from the engine, you should
(A) replace the oil cap
(B) run the engine for a moment and check the dipstick
(C) wipe off and replace the drain plug
(D) engage the emergency brake
IF YOU FINISH BEFORE THE TIME IS UP, YOU MAY CHECK
OVER YOUR WORK ON THIS PART ONLY.
STOP
ASVAB DIAGNOSTIC TEST
Part 5: Mathematics Knowledge (MK)
24
Minutes
— 25
Questions
Directions: In this section, you will be tested on your knowledge of
basic mathematics. For each question, select the best answer and
mark the corresponding oval on your answer sheet.
1. If 48 is divided by 0.08, the result is
(A) 0.06
(B) 0.6
(C) 60
(D) 600
2. If the number 9,899,399 is increased by 2,082, the result will be
(A) 9,901,481
(B) 9,901,471
(C) 9,902,481
(D) 9,902,471
3. The cube of 9 is
(A) 27
(B) 81
(C) 243
(D) 729
4. What is the value of (-ab)(a) when a = -2 and b = 3?
(A) −12
(B) −6
(C) 6
(D) 12
5. (x − 4)(x − 4) =
(A) x2 + 8x − 16
(B) x2 − 8x − 16
(C) x2 − 8x + 16
(D) x2 − 16x + 8
6. 0.123 × 104 =
(A) .0000123
(B) .00123
(C) 1.23
(D) 1,230
7.
(A) 2
(B) 4
(C) 6
(D) 8
8. A circle has a diameter of 6, an area of b square units, and a
circumference of c units. What is the value of b + c?
(A) 9π
(B) 15π
(C) 18π
(D) 42π
9. A bag contains 8 white, 4 red, 7 green, and 5 blue marbles. Eight
marbles are withdrawn at random. How many of the withdrawn
marbles are white if the chance of drawing a white marble is now 1
in 4?
(A) 3
(B) 4
(C) 5
(D) 6
10. Liza has 40 fewer than 3 times the number of books that Janice has.
If B is equal to the number of books that Janice has, which of the
following expressions shows the number of books that Liza and
Janice have together?
(A) 3B − 40
(B) 3B + 40
(C) 4B − 40
(D) 4B Correct+ 40
11. If the perimeter of a square is 32 meters, then what is the area of
the square, in square meters?
(A) 16
(B) 32
(C) 48
(D) 64
12. If x ≠ 0, then
(A) 4x4
(B) 4x3
(C) 3x4
(D) 3x3
13. A number is considered “blue” if the sum of its digits is equal to the
product of its digits. Which of the following is “blue”?
(A) 111
(B) 220
(C) 321
(D) 422
14. If x =
, what is the value of y when
?
(A)
(B) 4
(C) 16
(D) 64
15.
If line p above is parallel to line q, what is the value of x + y?
(A) 90
(B) 110
(C) 125
(D) 180
16. If 3ab = 6, what is the value of a in terms of b?
(A)
(B)
(C) 2b
(D) 2b2
17. For what value of y is 4(y − 1) = 2(y + 2)?
(A) 0
(B) 2
(C) 4
(D) 6
18.
In triangle RST above, if RS = RT, what is the degree measure of
angle S?
(A) 40
(B) 55
(C) 70
(D) cannot be determined from the information given
19. When D is divided by 15, the result is 6 with a remainder of 2. What
is the remainder when D is divided by 6?
(A) 0
(B) 2
(C) 3
(D) 4
20. If the average of 7 consecutive even numbers is 24, then the largest
number is
(A) 26
(B) 28
(C) 30
(D) 34
21. A box that has dimensions of 2 inches by 3 inches by 4 inches has a
total surface area of
(A) 24 square inches
(B) 26 square inches
(C) 48 square inches
(D) 52 square inches
22. If 100 ÷ x = 10n, then which of the following is equal to nx?
(A) 10
(B) 10x
(C) 100
(D) 10xn
23.
In the figure above, what is the value of x?
(A) 15
(B) 30
(C) 55
(D) 70
24. If 7! = 7 × 6 × 5 × 4 × 3 × 2 × 1, then 5! =
(A) 15
(B) 75
(C) 120
(D) 125
25. Melissa took 5n photographs on a certain trip. If she gives n
photographs to each of her 3 friends, how many photographs will
she have le ?
(A) 2n
(B) 3n
(C) 4n − 3
(D) 4n + 3
IF YOU FINISH BEFORE THE TIME IS UP, YOU MAY CHECK
OVER YOUR WORK ON THIS PART ONLY.
STOP
ASVAB DIAGNOSTIC TEST
Part 6: Electronics Information (EI)
9
Minutes
— 20
Questions
Directions: In this section, you will be tested on your knowledge of
electronics basics. For each question, select the best answer and
mark the corresponding oval on your answer sheet.
1. A load
(A) has very low resistance and conducts current throughout the
circuit
(B) is a device that converts electrical energy into heat, light, or
motion
(C) is a voltage source
(D) switches electrical current off and on
2. Which of the following symbols represents a photosensitive diode?
(A)
(B)
(C)
(D)
3. One
hertz is equivalent to
(A) one cycle per second of any continuous process
(B) an acceleration of 1 m/s2
(C) a change in frequency of one cycle per second per second
(D) the negative of the period
4. A(n)
is an element that freely conducts electricity.
(A) insulator
(B) conductor
(C) semiconductor
(D) molecule
5. Which of the following CANNOT describe an “earth ground” in
home electricity?
(A) a buried conduit
(B) a copper rod driven into the ground
(C) a device made to protect occupants from electrical shock
(D) a device for measuring electrical resistance
6. Electron flow theory states that
(A) electrons flow best through liquids
(B) electrons flow from areas of excess negative charge to areas of
less negative charge
(C) electrons flow from areas of excess positive charge to areas of
less positive charge
(D) electrons can only flow from one area to another if there is no
resistance
7. The “electrical pressure” that causes electrons to flow in one
direction through a conducting path is a result of
(A) a voltage
(B) a difference in resistance
(C) parallel paths
(D) a wire moving downhill
8. This is the symbol for which type of meter?
(A) voltmeter
(B) ammeter
(C) ohmmeter
(D) galvanometer
9. What type of circuit does this symbol represent?
(A) parallel circuit
(B) series-parallel circuit
(C) series circuit
(D) short circuit
10. Under a constant voltage, increasing resistance results in current
flow
(A) dropping
(B) rising
(C) staying the same
(D) changing direction
11. Increasing the voltage in a circuit and keeping resistance the same
will result in
(A) increased current flow
(B) decreased current flow
(C) current flow staying the same
(D) zero current flow
12. Several loads in series have different resistances. Given that the
same current flows through each of them, what relationship does
Ohm’s law predict between resistance and voltage drop?
(A) Larger voltage drops occur across loads with greater
resistances.
(B) Smaller voltage drops occur across loads with greater
resistances.
(C) Larger voltage drops occur across loads with lesser
resistances.
(D) An equal voltage drop occurs across each load in series,
independent of resistance.
13. Capacitive reactance decreases as electrical frequency
(A) decreases
(B) increases
(C) varies
(D) gets closer to DC
14. Which is the emitter in the transistor symbol below?
(A) 1
(B) 2
(C) 3
(D) 4
15. Which of the following CANNOT be used to make the magnetic field
in a coil of wire stronger?
(A) increasing the number of turns of wire in the coil
(B) increasing the current flowing through the coil
(C) inserting an iron core into the middle of the coil
(D) inserting a dielectric between each coil
16. Whenever current passes through a resistance,
o en generated.
(A) voltage
(B) capacitance
(C) heat
(D) light
17. The formula for Ohm’s Law is
(A) V = I × R
(B) V = I − R
(C) V = I + R
(D) V = I ÷ R
18. If current is able to pass through a diode, the diode must be
is most
(A) reverse-biased
(B) forward-biased
(C) open
(D) grounded
19. Transistors are turned on and off by voltages applied to their
(A) collector
(B) emitter
(C) base
(D) cathode
20. If each resistor in this circuit equals 1,000 ohms, what is the total
resistance in this circuit?
(A) 250 ohms
(B) 500 ohms
(C) 1,000 ohms
(D) 4,000 ohms
IF YOU FINISH BEFORE THE TIME IS UP, YOU MAY CHECK
OVER YOUR WORK ON THIS PART ONLY.
STOP
ASVAB DIAGNOSTIC TEST
Part 7: Auto and Shop Information
(AS)
11
Minutes
— 25
Questions
Directions: In this section, you will be tested on your knowledge of
automotive and shop basics. For each question, select the best
answer and mark the corresponding oval on your answer sheet.
1. High-intensity ultraviolet light is generated during
.
(A) welding
(B) sawing
(C) soldering
(D) drilling
2. Most drill bits are made to cut when
(A) rotating to the right when viewed from the top
(B) rotating to the le when viewed from the top
(C) rotating to the right when viewed from the bottom
(D) oscillating
3. A motor oil with a
suited for a diesel engine.
prefix for its quality rating would be
(A) CD
(B) SA
(C) SJ
(D) DM
4. Coil-on-plug ignition systems eliminate the need for
(A) secondary coil winding
(B) spark plug wires
(C) spark plugs
(D) primary coil winding
5. A DOHC V-8 engine would have a total of
(A) two
(B) three
(C) four
(D) eight
6. What type of file is depicted below?
(A) smoothing file
(B) bastard file
(C) round rasp
(D) flat rasp
7. Cutting torches use a mixture of
to produce a high-temperature flame.
camsha s.
(A) nitrogen
and acetylene
(B) nitrogen
and oxygen
(C) acetylene
and helium
(D) acetylene
and oxygen
8. All cars are currently being built with
systems.
electrical
(A) direct current
(B) alternating current
(C) negative ground
(D) both direct and alternating current
9. As lead-acid batteries discharge, their electrolyte gradually turns to
(A) sulphuric acid
(B) water
(C) lead peroxide
(D) none of the above
10. The camsha turns at
the speed of the engine’s
cranksha .
(A) one-half
(B) one-fourth
(C) twice
(D) triple
11. An outside micrometer can be used to measure all of the following
EXCEPT
(A) the distance between two wooden posts
(B) the thickness of flat objects
(C) the outside diameter of small cylindrically shaped objects
(D) the outside diameter of small spherical objects
12. Which of the following is the most common type of pliers?
(A)
(B)
(C)
(D)
13. What type of saw is depicted below?
(A) rip saw
(B) crosscut saw
(C) coping saw
(D) back saw
14. Engine temperature is controlled by the
(A) electrical system
(B) water pump
(C) radiator
(D) thermostat
15. This image depicts what stroke in the four-stroke cycle?
(A) intake stroke
(B) compression stroke
(C) power stroke
(D) exhaust stroke
16. The three elements needed to initiate combustion are
(A) air, light, and fuel
(B) air, fuel, and an ignition source
(C) air, compression, and an ignition source
(D) air, heat, and compression
17. A four-cylinder engine’s firing order always starts with cylinder
number
(A) 1
(B) 2
(C) 4
(D) 8
18.
cylinders will fire in one revolution of a six-cylinder
engine.
(A) Two
(B) Three
(C) Four
(D) Eight
19. Which of the following is the LEAST likely to be found in an auto
mechanic’s toolbox?
(A)
(B)
(C)
(D)
20. Most solders are an alloy of
.
(A) tin
and copper
(B) tin
and lead
(C) copper
and lead
(D) brass
and copper
21. A lead-acid battery has lead plates immersed in electrolyte
composed of
and water.
(A) citric acid
(B) hydrochloric acid
(C) carbolic acid
(D) sulphuric acid
22. The starter motor’s drive gear engages with the engine’s
(A) flywheel ring gear
(B) cranksha
(C) vibration damper
(D) timing chain
23. Sockets come in both
point designs
(A) 6 and 12
(B) 7 and 13
(C) 5 and 10
(D) 1 and 2
24. The stoichiometric, or ideal, air-fuel ratio is
(A) 10:1
(B) 17:1
(C) 14.7:1
(D) 17:4.2
25. With disc brakes, the
rotates with the vehicle’s wheels.
(A) brake rotor
(B) brake caliper
(C) brake drum
(D) wheel cylinder
IF YOU FINISH BEFORE THE TIME IS UP, YOU MAY CHECK
OVER YOUR WORK ON THIS PART ONLY.
STOP
ASVAB DIAGNOSTIC TEST
Part 8: Mechanical Comprehension
(MC)
19
Minutes
— 25
Questions
Directions: In this section, you will be tested on your knowledge of
mechanics and basic physics. Select the best answer for each
question and mark the corresponding oval on your answer sheet.
1. Torque is
(A) the degree to which a force causes an object to rotate
(B) the same as horsepower
(C) a push or pull
(D) a force that travels in a circle
2. Speed is different from velocity because
(A) speed is measured in metric units while velocity is measured in
English units
(B) velocity involves both speed and direction
(C) speed involves both velocity and direction
(D) velocity is a scalar quantity
3. Compared to a smaller mass, a larger mass requires
force to achieve the same acceleration rate.
(A) less
(B) more
(C) the same
(D) varying
4. Which of the following statements about force is NOT true?
(A) Force is a scalar quantity
(B) Force is a push or pull
(C) Greater force results in greater acceleration
(D) Smaller masses require less force to achieve the same
acceleration as larger masses
5. Mechanical advantage is the advantage gained by the use of
in transmitting force.
(A) power
(B) a transformer
(C) a mechanism
(D) an engine
6. A hockey puck sliding on the ice
(A) has no net force acting on it
(B) would slide forever if the rink was long enough
(C) has speed, but not velocity
(D) experiences kinetic friction
7. If gear A turns in a counterclockwise direction, how does gear B
turn?
(A) in a counterclockwise direction
(B) in a clockwise direction
(C) remains stationary
(D) turns more slowly than gear A
8. Which of the following statements about weight is NOT true?
(A) Weight increases closer to Earth’s surface.
(B) Weight is totally dependent on mass.
(C) Weight is greater on planets with greater mass.
(D) Weight varies from location to location.
9. While attempting to push a heavy box across the floor,
(A) the amount of force required to start the box sliding is less
than that required to keep it sliding
(B) the amount of work being done is not dependent on how far
the box moves
(C) the coefficient of static friction is dependent on the nature of
the surface the box is resting on
(D) the mass of the box does not affect the amount of force
required
10. Which of the following represents the mechanical advantage of a
wheel and axle system where the driven wheel has a radius of 10"
and the drive wheel has a diameter of 5"?
(A) 4:1
(B) 2:1
(C) 1:2
(D) 1:4
11. If it takes a force of 20 pounds to stretch the spring one inch, how
much force must be applied to stretch the spring three inches?
(A) 180 pounds
(B) 60 pounds
(C) 20 pounds
(D) 6.67 pounds
12. In order to apply more torque to a bolt, a mechanic could
(A) use a longer wrench
(B) apply less force to the wrench
(C) use a shorter wrench
(D) move the wrench more quickly
13. A vehicle travels at a constant speed on the highway. It can be said
that
(A) its acceleration rate is less than zero
(B) the net force acting on the vehicle is zero
(C) the force applied by the vehicle’s drive wheels is greater than
the forces that act to slow the vehicle
(D) it is accelerating at a constant rate
14. The two water towers below are of equal size and height above the
ground. If both towers are completely full and their valves are
opened, which of the following statements is true?
(A) The two towers will release the same amount of water.
(B) Tower B will release more water than tower A.
(C) Tower A will release water three times as fast as tower B.
(D) Tower A will release more water than tower B.
15. Two signs of equal weight are attached to a beam, using cords of
equal length. Which of the following statements is true?
(A) All cords have the same amount of tension because the signs
are of equal weight.
(B) The cord holding sign A is under twice the tension of the cords
holding sign B.
(C) The cords holding sign B are under
the tension of the cord holding sign A.
(D) The cords holding sign B are under
the tension of the cord holding sign A.
16. The illustration below is an example of which kind of lever?
(A) first-class lever
(B) second-class lever
(C) third-class lever
(D) this is not a lever
17. If a vehicle accelerates from a standstill at a rate of
its velocity a er 10 seconds will be
(A)
(B)
(C)
(D)
18. A wheelbarrow, as pictured below, is an example of
(A) a second-class lever
(B) a pulley system
(C) a third-class lever
(D) a crank
19. The gears in the illustration all have the same number of teeth. If
gear X moves clockwise, which statement about gear Y is true?
(A) Gear Y moves counterclockwise.
(B) Gear Y moves twice as fast as gear X.
(C) Gear Y moves more
slowly than gear X.
(D) Gear Y moves clockwise.
20. One pound of force is applied to move an object a distance of one
foot. How much work has been done?
(A) 1 foot-pound
(B) 1 watt
(C) 2 foot-pounds
(D) 1 hertz
21. Which of the following statements about energy is NOT true?
(A) Energy cannot be created.
(B) The amount of energy in the universe is slowly diminishing.
(C) Energy cannot be destroyed.
(D) Energy can be converted from one form into another.
22. How many feet must the right end of the rope be pulled to raise
weight W by 2 feet?
(A) 1
(B) 2
(C) 4
(D) 8
23. Which of the following is NOT a true statement about the principles
that underlie hydraulics?
(A) Liquids conform to the shape of their container.
(B) A liquid can be dramatically compressed in order to increase
the amount of force the liquid can transfer.
(C) A liquid is effectively incompressible.
(D) When pressure is applied to a completely enclosed fluid, this
pressure is transmitted to all parts of the fluid and the
enclosing walls.
24. Efficiency of a machine is determined by
(A) how much horsepower it can produce
(B) how much energy it consumes
(C) how much of the source energy is converted into usable
energy
(D) how long the machine can operate at full output
25. In order to hit a baseball so that the ball has greater velocity, the
player must
(A) hit the ball with less force
(B) make contact with the ball for a longer period of time
(C) apply more torque to the ball
(D) hit the ball so that it travels at roughly a 45° angle relative to
the ground
IF YOU FINISH BEFORE THE TIME IS UP, YOU MAY CHECK
OVER YOUR WORK ON THIS PART ONLY.
STOP
ASVAB DIAGNOSTIC TEST
Part 9: Assembling Objects (AO)
15
Minutes
— 25
Questions
Directions: In this section, you will be tested on your ability to
determine how an object will look when its parts are put together.
For each question, select the best answer and mark the
corresponding oval on your answer sheet.
For questions 1–12:
Which figure best shows how the objects on the le will appear if they
are fit together?
1.
(A)
[image]
(B)
(C)
(D)
2.
(A)
(B)
(C)
(D)
3.
(A)
(B)
(C)
(D)
4.
(A)
(B)
(C)
(D)
5.
(A)
(B)
(C)
(D)
6.
(A)
(B)
(C)
(D)
7.
(A)
(B)
(C)
(D)
8.
(A)
(B)
(C)
(D)
9.
(A)
(B)
(C)
(D)
10.
(A)
(B)
(C)
(D)
11.
(A)
(B)
(C)
(D)
12.
(A)
(B)
(C)
(D)
For questions 13–25:
Which figure best shows how the objects on the le will touch if the
letters for each object are matched?
13.
(A)
(B)
(C)
(D)
14.
(A)
(B)
(C)
(D)
15.
(A)
(B)
(C)
(D)
16.
(A)
(B)
(C)
(D)
17.
(A)
(B)
(C)
(D)
18.
(A)
(B)
(C)
(D)
19.
(A)
(B)
(C)
(D)
20.
(A)
(B)
(C)
(D)
21.
(A)
(B)
(C)
(D)
22.
(A)
(B)
(C)
(D)
23.
(A)
(B)
(C)
(D)
24.
(A)
(B)
(C)
(D)
25.
(A)
(B)
(C)
(D)
IF YOU FINISH BEFORE THE TIME IS UP, YOU MAY CHECK
OVER YOUR WORK ON THIS PART ONLY.
STOP
CONGRATULATIONS! YOU HAVE COMPLETED THE DIAGNOSTIC TEST.
Answers and Explanations
PART 1: GENERAL SCIENCE (GS)
1. A
Proteins are necessary for the body’s maintenance, growth, and repair.
Carbohydrates and fats are used primarily for energy. Vitamins are
necessary for the functioning of various enzymes.
2. C
Water boils at 212 degrees on the Fahrenheit scale at sea level. On the
Celsius scale, it boils at 100 degrees and on the Kelvin scale at 373 K.
3. D
The process by which animals convert oxygen (and sugars) into carbon
dioxide and water is called respiration. The reverse process, by which
plants convert carbon dioxide and water into sugar and oxygen, is called
photosynthesis.
4. B
Veins carry blood from capillaries toward the heart. Arteries carry blood
away from the heart. Ventricles are the lower chambers of the heart. Red
blood cells are the component of blood that carries oxygen.
5. B
Iron forms rust when water (or an even better electrolyte) turns iron and
oxygen into iron oxide (Fe2O3); this is a chemical process. Helium and
neon are both inert noble gases, so they do not react chemically. When
sugar dissolves in water, the sugar particles become evenly distributed
throughout the water, forming a solution. However, neither is changed
chemically. The sugar can be restored by boiling off the water. Ice
melting does not alter the chemistry of H2O.
6. A
Type O negative is the universal donor, which means that type O
negative blood can be given to anybody without an adverse reaction.
7. D
Blood enters the right atrium of the heart from the vena cava.
8. A
The more basic (that is, alkaline) a substance is, the higher the pH. A
substance with a pH of 7 is neutral, like pure water. A substance with a
pH of less than 7 is acidic, and a substance with a pH of greater than 7 is
basic/alkaline. Look in the answer choices for a base. Of the substances
listed, ammonia is the most basic or alkaline.
9. C
Of the various digestive organs, the small intestine does the most work
in breaking the food down into usable nutrients. Food is broken down
completely by enzymes produced in the walls of the small intestine, in
the pancreas, and in the liver.
10. D
In the male reproductive system, the testes produce sperm. In the
female reproductive system during ovulation, an egg, or ovum, is
released from the ovary and begins to travel through the oviduct
(fallopian tube) and into the uterus.
11. D
A gene is defined as the most basic unit of inheritance. A genotype is the
combination of alleles that codes for a particular trait. A phenotype is
the physical expression of a particular genotype. Chromosomes are
tightly coiled strands of DNA that contain multiple genes.
12. C
Shale, which is derived from clay sediments, is an example of
sedimentary rock.
13. C
An autotroph is known as a producer or self-feeder because it can
produce its own food. This is generally done through photosynthesis or
chemosynthesis. A saprotroph is a decomposer, a hetereotroph relies on
other organisms to be its food, and a scavenger feeds on decaying flesh.
14. C
A vulture is considered a scavenger. These animals mostly consume
refuse and decaying organic matter, especially carrion, which is
decaying flesh.
15. B
Igneous rocks are formed from the cooling of lava and include obsidian,
granite, basalt, and others.
16. C
A lunar eclipse happens when the Moon passes through the Earth’s
shadow. During a lunar eclipse, the Earth lies between the Moon and
Sun.
17. A
The prefix centi– indicates hundredth. One thousandth of a meter is
called a millimeter. 10 meters is a decameter and 100 meters is a
hectometer.
18. D
Momentum is the tendency of an object to continue moving in the same
direction. Velocity is the rate at which an object changes position.
Acceleration is the rate of change of velocity. Force is the push or pull
that forces an object to change its speed or direction.
19. D
Visible light is composed of different colors each with a different
frequency. Red has the lowest frequency, and violet has the highest
frequency.
20. A
The major portion of an atom’s mass consists of neutrons and protons.
Electrons, positrons, neutrinos, and other subatomic particles have
negligible masses.
21. C
Arthropods represent a large phylum of the animal kingdom
characterized by chitinous exoskeletons, segmented bodies, and jointed
legs. Examples include crabs, centipedes, and spiders, but not the sea
urchin, which belongs to the phylum Echinodermata.
22. A
Table salt (NaCl) is an ionic compound because each chlorine atom
borrows an electron from each sodium atom. This results in very strong
ionic bonds that enable salt to form a tightly bound crystalline structure
when in the solid form. When salt is placed in water, however, the
crystalline structure breaks down, and the individual sodium and
chlorine ions are both able to dissociate into the water.
23. C
Over the course of 24 hours, the Earth rotates 360°, or one complete
rotation, about its axis.
24. C
The Monera kingdom is considered the most primitive kingdom because
its organisms are prokaryotic—that is, their cells lack nuclei.
25. B
The phylum Chordata contains animals with vertebrae. (In human
beings, the vertebrae are the bones that make up the spine.) Animalia is
the kingdom that includes humans. Mammalia is the class that includes
humans. Primata is an order that includes primates (such as humans).
Answers and Explanations
PART 2: ARITHMETIC REASONING (AR)
1. C
This question asks you to determine the sale price of a camera that
normally sells at $160 and is discounted 20%. To solve, determine what
20% of $160 equals. Rewrite 20% as a decimal. 20% = 0.20. So 20% of $160
= 0.20 × $160 = $32The sale price of the camera would be $160 – $32 =
$128, choice (C).
2. B
First, set up the rate as a proportion, where x is the number of stations.
Then, convert the units.
Cross-multiply and solve for x.
180 = 10x
18 = x
3. B
In this question, the ratio is implied: for every
inch of map there is 1 real
mile, so the ratio of inches to the miles they represent is always
to 1.
Therefore, you can set up the proportion:
Now
inches =
inches.
Set up a proportion:
inches
Cross-multiply:
4. D
You can express the ratio of baseballs to golf balls as
. Since you know
the number of baseballs, you can set up a proportion:
where x is the number of golf balls. To solve, cross-multiply to get 2x = 90,
or x = 45.
5. D
The total cost of the taxi ride equals $36 + (25% of $36), or $36 + (.25 × $36)
= $36 + $9 = $45. If four people split the cost equally, then each person
paid
, or $11.25 each.
6. A
Find the number of seconds in an hour and then multiply this by the
distance the car is traveling each second. There are 60 seconds in a minute
and 60 minutes in one hour; therefore, there are 60 × 60, or 3,600, seconds
in an hour. In one second the car travels
car will travel 3,600 ×
kilometers; in one hour the
or 36 kilometers.
7. B
Subtracting a negative number is the same as addition, so 20 − (−5) is
really 20 + 5 = 25.
8. C
If Ms. Smith’s car averages 35 miles per gallon, she can go 35 miles on 1
gallon. To go 700 miles she will need , or 20 gallons of gasoline. The price
of gasoline was $1.25 per gallon, so she spent 20 × $1.25, or $25, for her
trip.
9. D
Be careful with a question like this one. You’re given the percent decrease
(25%) and the new number (72), and you’re asked to reconstruct the
original number. Don’t just take 25% of 72 and add it on. That 25% is
based not on the new number, 72, but on the original number—the
number you’re looking for. The best way to do a problem like this is to set
up an equation:
Alternatively, you can use the answer choices to determine the correct
answer. The original number of jelly beans has to be reducible by 25%, or
. That means the original number of jelly beans has to be a multiple of 4
(or else you'd be reducing by pieces of jelly beans). Only the correct
answer, 96, is a multiple of 4.
10. B
The time it takes to complete the entire exam is the sum of the time spent
on the first half of the exam and the time spent on the second half. The
time spent on the first half is
of the time spent on the second half. If S
represents the time spent on the second half, then the total time spent is
. You know this total time is one hour, or 60
minutes. Set up a simple equation and solve for S.
So the second half takes 36 minutes. The first half takes
of this, or 24
minutes. You could also find the first half by subtracting 36 minutes from
the total time, 60 minutes.
11. A
You’re asked what percent of the new solution is alcohol. The part is the
number of ounces of alcohol; the whole is the total number of ounces of
the new solution. There were 25 ounces originally. Then 50 ounces were
added, so there are 75 ounces of new solution. How many ounces are
alcohol? 20% of the original 25-ounce solution was alcohol. 20% is
, so
of 25, or 5 ounces are alcohol. Now you can find the percent of alcohol
in the new solution:
12. A
To find probability, determine the number of desired outcomes and divide
that by the number of possible outcomes. The probability formula looks
like this:
In this case, Marty is pulling one pen at random from his knapsack, and
you want to determine the probability that the pen is either red or black.
There are 5 blue pens, 6 black pens, and 4 red pens in the knapsack. Let’s
return to the probability formula:
13. D
Be careful with combined percent increase. You cannot just add the two
percents, because they’re percents of different bases. In this instance, the
100% increase is based on the 1980 population, but the 50% increase is
based on the larger 1990 population. If you just added 100% and 50% to
get 150%, you would have chosen a wrong answer.
The best way to do a problem like this one is to pick a number for the
original whole and just see what happens. The best number to pick here is
100. (That may be a small number for the population of a country, but
reality is not important—all that matters is the math.)
If the 1980 population was 100, then a 100% increase would put the 1990
population at 200. And a 50% increase over 200 would be 200 + 100 = 300.
Since the population went from 100 to 300, that’s a percent increase of
200%.
14. B
To learn the worker’s overtime rate of pay, first figure out her regular rate
of pay. Divide the amount of money made, $200, by the time it took to
make it, 40 hours. $200 ÷ 40 hours = $5 per hour. That is the normal rate.
The worker is paid
times her regular rate during overtime, so when
working more than 40 hours, she makes
× $5 per hour = $7.50 per hour.
Now figure out how long it takes the worker to make $230. It takes her 40
hours to make the first $200. The last $30 are made at the overtime rate.
Since it takes one hour to make $7.50 at this rate, you can figure out the
number of extra hours by dividing $30 by $7.50 per hour: $30 ÷ $7.50 per
hour = 4 hours. The total time needed is 40 hours plus 4 hours, or 44 hours.
15. A
The calculations aren’t too bad on this one. The most important thing to
keep in mind is that you’re solving for 75% of x and not for x itself. First,
you are told that 50% of x is 150. That means that half of x is 150, and that
x is 300. So 75% of x = 0.75 × 300 = 225.
16. D
This is a question where Backsolving (plugging in an answer choice to see
if it’s correct) can save you a lot of time. Let’s start with choice (B) and see
if it works. If (B) is correct, an adult’s ticket would cost $3.00, and a child’s
ticket would cost $1.50. The total fare you're asked for is for two adults
and three children. If an adult’s fare was $3.00, that total fare would be
2($3.00) + 3($1.50) = $6.00 + $4.50 = $10.50. That’s too low, since the
question states that the total fare is $14.00.
Now see what happens if an adult fare was more expensive. If (D) was
correct, an adult’s ticket would cost $4.00 and a child’s ticket would cost
$2.00. The total fare would equal 2($4.00) + 3($2.00) = $8.00 + $6.00 =
$14.00. That’s the total fare you’re looking for, so (D) is correct.
17. C
To find the prime factorization of a number, find one prime that will go
into the number (here 2 is a good place to start). Express the number as
that prime multiplied by some other number.
140 = 2 × 70
Then keep breaking down the larger factor until you are le with only
prime numbers.
140 = 2 × 2 × 35
140 = 2 × 2 × 5 × 7
18. A
When the painter and his son work together, they charge the sum of their
hourly rates, $12 + $6, or $18 per hour. Their bill equals the product of this
combined rate and the number of hours they worked. Therefore $108
must equal $18 per hour times the number of hours they worked. Divide
$108 by $18 per hour to find the number of hours. $108 ÷ $18 = 6.
19. C
The exclamation mark indicates a factorial. A factorial is an integer
multiplied by every smaller integer, down to the number 1, like this: 4! = 4
× 3 × 2 × 1 = 24
20. B
Compute the cost of parking a car for 5 hours at each garage. Since the
two garages have a split-rate system of charging, the cost for the first hour
is different from the cost of each remaining hour.
The first hour at garage A costs $8.75
The next 4 hours cost 4 × $1.25 = $5.00
The total cost for parking at garage A = $8.75 + $5.00 = $13.75
The first hour at garage B costs $5.50
The next 4 hours cost 4 × $2.50 = $10.00
The total cost for parking at garage B = $5.50 + $10.00 = $15.50
So the difference in cost = $15.50 − $13.75 = $1.75, (B).
21. C
Set up a proportion:
An hour is 60 minutes; one third of that is 20 minutes. So
hours is 8
hours and 20 minutes.
22. B
This problem sets up relationships among large, medium, and small sodas
—2 large sodas are equal to 3 medium sodas, and 2 medium sodas are
equal to 3 small sodas. How many small sodas equal 8 large sodas? Well, 2
larges equal 3 mediums, so 12 mediums must equal 4 × 2 or 8 large sodas.
You now can find how many small sodas represent 12 mediums. Since 2
mediums are the same as 3 small sodas, 12 mediums must equal 6 × 3 or
18 small sodas.
23. D
If you change each digit 5 into a 7 in the number 258,546, the new number
would be 278,746. The difference between these two numbers would be
278,746 − 258,546 = 20,200.
24. B
Since 1 pound of lumber costs $4.00,
pounds of lumber cost 2.25 ×
$4.00 = $9.00. Then add 7% sales tax to $9.00. Find 7% of $9.00 by
multiplying 0.07 × $9.00 = $0.63. Add $0.63 to $9.00 to get $9.63, choice (A).
25. D
The question asks which of five ratios is equivalent to the ratio of
to
. Since the ratios in the answer choices are expressed in whole
numbers, turn this ratio into whole numbers. Start by turning the ratio
into improper fractions:
Multiply both sides of the ratio by 4.
= 13 : 21
26. D
Set up the proportion.
Cross-multiply.
x = 72
x = 72 ×
x = 192
27. C
You can save valuable time by estimating on this one. Pay special
attention to how much you have le and how much you’ve already spent.
If Eva spent
had
of her salary and was le with $420, that means that she
le , and if Eva’s salary is x dollars, then
x = $420. That means
that $420 is a little more than half of her salary. So her salary would be a
little less than 2($420) = $840. Choice (C), $720, is a little less than $840. So
(C) works perfectly, and it’s the correct answer here.
28. C
The key to this question is that while the value of the stock decreases and
increases by the same amount, it doesn’t decrease and increase by the
same percent. When the stock first decreases, that amount of change is
part of a larger whole. If the stock were to increase to its former value, that
same amount of change would be a larger percent of a smaller whole.
Pick a number for the original value of the stock, such as $100. (Since it’s
easy to take percents of 100, it’s usually best to choose 100.) The 20%
decrease represents $20, so the stock decreases to a value of $80. Now in
order for the stock to reach the value of $100 again, there must be a $20
increase. What percent of $80 is $20? It’s
× 100%, or
× 100%, or
25%.
29. C
This is a combined work problem. Joan can shovel the whole driveway in
50 minutes, so each minute she does
of the driveway. Mary can shovel
the whole driveway in 20 minutes; in each minute she does
of the
driveway. In one minute they do:
If they do
in
of the driveway in one minute, they do the entire driveway
minutes. (If you do
the reciprocal of
of a job in 1 minute, you do the whole job in
, or 2 minutes.) So all that remains is to round
to the nearest integer. Since
=
,
off
is approximately 14. It
takes about 14 minutes for both of them to shovel the driveway.
30. B
You’re told that Eileen earns $280 per week. Kelly earns $50 more than
Eileen, so Kelly earns $280 + $50 = $330 per week. June’s salary is $70 less
than Kelly’s, so June earns $330 − $70 = $260 per week, and (B) is correct.
Answers and Explanations
PART 3: WORD KNOWLEDGE (WK)
1. C
Noble means “related to high rank or social class.” The aristocracy is
composed of the highest classes in society; therefore, choice (C) is
correct.
2. D
The sentence draws a contrast between John initially disagreeing with
Megan and then conceding her point. That context suggests that
concede likely means the opposite of disagree. Admit is the best match:
to admit a point is to agree with it.
3. B
The verb form of goad means to “prod into action or coerce.” Of the
answer choices, only provoke approximates this meaning.
4. C
The word herd refers to a group of people or animals. Similarly, a pack is
a group of people or animals, like a wolf pack or a scout pack.
5. D
If you know that an EMT is a rescue technician, then you may grasp the
idea that panic is not allowed. Viable then can mean “capable of survival
or success.” Only (D), workable, which means “able to produce the
desired result,” suggests that meaning.
6. C
Judicious means “possessing or displaying good judgment,” or in other
words, being “wise.”
7. D
Hesitating can mean “pausing before doing something,” or sometimes
“reluctant or indecisive.” Among the answer choices available, the only
possible correct answer is (D), pausing.
8. A
You probably know the root word false as meaning “wrong,” or in
reference to a lie. The textbook definition is to misrepresent. Looking at
the possible answer choices, choice (A), fabricating, which means
“making up,” is the best possible answer.
9. C
The word hollow means “lacking a center or empty.”
10. C
The verb to coax means “to try to persuade.” Of the answer choices, only
(C), plead, approaches being correct.
11. B
The root of the word monotonous is mono meaning one. Something
monotone is in one flat tone and is completely lacking in variety. Boring
would be another way to say this.
12. C
The word consternation means “anxiety or dismay.” Of the answer
choices, frustration is the closest match. The context of the sentence
hints at this meaning, because the material the students are learning is
difficult.
13. A
Savory in reference to food means “appetizing to taste.” Choice (A), tasty,
is the best answer.
14. B
Renown means “fame or reputation.”
15. B
A raconteur is someone who tells stories. The word even sounds a little
like “recount.”
16. D
To quench something is to “sate or satisfy” it.
17. A
The word polarized has the same root as polar. Think of “polar
opposites” and you will be on the right track. In this case, choice (A),
split, is closest in meaning to polarized.
18. C
Precise means “exact or specific.”
19. B
Terrain comes from the root terra or earth. So of the answer choices,
only landscape would be appropriate. Landscape is the ground in view.
20. D
Terminal means “relating to an end, limit, or boundary.” Choice (D), final,
is most similar in meaning.
21. D
Augment means to “enhance something already developed.”
22. A
Something involuntary is something done “without plan or
accidentally”–in other words, unintentionally.
23. B
The noun collusion refers to “an agreement of an illicit or secret nature.”
The prefix con– (which here appears as col–) is a useful hint here, since it
means together: people who collude agree to act together.
24. C
Tenacity means showing “persistence and determination.” The word
root ten relates to holding, so you could guess that tenacity might mean
something like “holding on.”
25. D
Tactile means “relating to the sense of touch.” Of the answer choices,
(D), tangible, is the most similar in meaning to the original word. In fact,
tactile and tangible come from the same root: in Latin, tangere means
“to touch.”
26. C
To portend is to “foreshadow or foretell,” as an omen or advance
warning sign. Here, predict is the closest match.
27. A
To germinate means to “sprout or bud, as a plant.”
28. B
Restore has the prefix re–, meaning “again.” Thus, restore means “bring
back something that had been lost.” Of the choices given, both (B) and
(D) refer to affecting change on something. But of the two, only (B),
invigorate, means to “renew.”
29. D
A filament is a “thread or string that is very thin.”
30. C
Mutate is a word you’ve probably seen before. Science-fiction movies
and comic books o en have mutated characters (like the Teenage
Mutant Ninja Turtles or Godzilla). The word means “something that has
changed from its original state.” Of the choices given, (C), altered, is the
best choice.
31. B
The adjective dynamic means “constantly changing or exciting.” The
word yet in the sentence is a clue that you are looking for a word that
contrasts with calm, making exciting a good choice.
32. C
Congeal means to “solidify, coagulate, or harden.”
33. D
To reconnoiter means to “make a preliminary inspection,” or “see before
others.” Of the answer choices, only (D), scout, means the same thing as
the given word.
34. A
The verb accrue means to “accumulate over time as a result of growth.”
35. D
An innate trait is one that is inherent or natural.
Answers and Explanations
PART 4: PARAGRAPH COMPREHENSION (PC)
1. B
The main idea of a passage is the most important idea conveyed by the
author. Choice (B) pinpoints the author’s main point. Choice (C) distorts
a detail from the passage. Choice (A) is not mentioned in the passage.
The author states that science was extremely popular in the nineteenth
century, which implies that science fiction was as well, but no direct
information is given about the popularity of science fiction. Choice (D) is
incorrect because there is no mention of Poe and Doyle being scientists.
2. C
The answer to a Detail question such as this will be a paraphrase of what
you find in the passage. You are told that reading shows students how
words are used in sentences, so (C) is correct. (A) is incorrect because
adults are never mentioned. (B) also was not stated in the passage. (D)
does not answer the question and is not necessarily true based on the
information given.
3. A
Wrong answer choices on Global questions (that is, questions that ask
about the passage’s topic or main idea) are o en too broad or too
specific. (B) is too broad because the passage is not about all American
art movements, only the Hudson River School movement. (C) is too
specific because the influence of European painters is just one detail
mentioned, while (A), the history of the Hudson River School of painters,
is being described. (D) is incorrect because nationalism is not the focus
of the passage.
4. D
This is the central idea of the passage. (If a passage begins or ends with a
recommendation, that recommendation will o en be the main idea.)
The author does imply that people should not base their decisions on
advertisements, choice (B), but that is a detail rather than the main idea.
Choice (A) is the opposite of the detail stated in the passage. Choice (C)
is too broad. The passage is primarily concerned with computer
purchase decisions, not life in general.
5. A
It is important on Vocabulary-in-Context questions not to rely on your
vocabulary knowledge alone for the word in question, but instead to
choose an answer that best represents how the word is being used in
the paragraph. Bleak can be used to mean cold, choice (C), or
depressing, which might make choice (B) seem appealing. But only
choice (A) does not alter the meaning of the sentence when plugged in:
“the empty landscape and broad skies.”
6. D
Since the answer to a Detail question can be found in the text, the clause
“nearly all her works are portrayals of nature” would direct you to
choice (D). Choices (A), (B), and (C) all state things that were never
mentioned in the passage, a characteristic typical of wrong answer
choices to Detail questions.
7. C
The text states that the Copernican model of the solar system describes
that planets are revolving around the Sun, choice (C). This is
contradicted by choice (B). (A) and (D) are not mentioned.
8. D
Toby is smiling while he waits for his father, already holding his baseball
glove and ball. He is eager, choice (D), to get to the game. Choice (A) is
distracting since it is sad that it might be the last game that Toby’s father
will be able to attend, but the descriptive language of the passage
supports eagerness and not sadness: the sun rushes into the room, now
the birds are appearing. Toby is smiling, so there is no evidence of him
being uneasy, choice (C). He is anxiously waiting for his father, which
contradicts his being careless, choice (B).
9. A
Since the body can survive without food longer than it can survive
without (B) drinking or (C) breathing, eating is the least essential to
survival. Choice (A) is correct. (D) is incorrect because excretion is not
mentioned in the passage.
10. C
For Inference questions you should read the entire passage, and it is
o en best to attack each answer choice and eliminate those that do not
follow from the passage. (B) clearly contradicts the author’s words. You
have no information about how the author feels about television
anchors, so (D) is unsupported. (A) goes beyond the scope of the
passage, and may or may not be true based on what you have read. The
correct answer will be something that must be true based on what’s
given, like choice (C).
11. A
This is a Detail question, which means that you can look up the answer
in the text. The poems “were intended to be sung or recited, not written
down,” so they were mainly an oral form, choice (A). (B), which states
that Greek poetry was unlike those of other societies, contradicts the
passage. (C) and (D) are not mentioned.
12. C
The correct choice for a Global question will express what the author
believes. The passage states that remarkable progress has been made in
artificial intelligence, so choice (C) is correct. While the author discusses
the difference of opinion between those who believe that there will
eventually be a computer capable of intelligent thought and those who
do not, she does not assert the truth of either statement, so choice (A) is
incorrect. Be wary of answer choices such as (D) that use extreme
language. Chess is not the main focus of the passage, so choice (B) is
incorrect.
13. B
This is a Global question, so either the correct answer will make so much
sense you will want to pick it, or you can eliminate wrong answer
choices because they are too broad, too specific, or otherwise don’t
properly describe the passage. Here the correct answer choice does
make a lot of sense. The passage describes how coral reefs are created,
so choice (B), the formation of coral reefs, describes the passage well.
Choice (A) is out because “varieties” of animal life are nowhere
described. (C) is wrong because “death cycles” of coral reefs are never
touched upon. And (D) is far too narrow; there’s only the barest
reference in the passage to “the physical beauty” of coral reefs.
14. D
For this Detail question, you just want to pick the answer choice that
best paraphrases the relationship between the coral and algae as
described in the passage. The passage states that the “two organisms
form a mutually beneficial relationship”; in other words, the relationship
is cooperative, choice (D).
15. C
For correct sequence questions, look up the answer in the text.
According to the passage, when the engine is fully drained, you should
wipe off and replace the drain plug, choice (C).
Answers and Explanations
PART 5: MATHEMATICS KNOWLEDGE (MK)
1. D
A question like this one tests your ability to work with decimals.
the same as
is
= 600. (D) is correct. When dividing by a decimal, be
sure to move the decimal place the same number of spaces for both
numbers.
2. A
Be careful with your number crunching here. 9,899,399 + 2,082 =
9,901,481, choice (A).
3. D
The cube of a number is that number multiplied by itself three times. So
the cube of 9 would be 9 × 9 × 9 = 729, choice (D).
4. A
Plug in the values for a and b and remember your order of operations
when working through your calculations. When a = −2 and b = 3,
(−ab)(a) = [− (−2) × 3](−2)
= (−[−6])(−2)
= (6) × (−2) = −12, choice (A).
5. C
This is a classic product of two binomials. Remember to FOIL, and you’re
good to go.
(x − 4)(x − 4)
= (x)(x) + (x)(−4) + (− 4)(x) + (−4)(−4)
= x2 − 4x − 4x + 16
= x2 − 8x + 16.
Choice (C) is correct. If you recognized this as one of the classic
quadratics, a binomial squared, you could have answered this correctly
without using FOIL.
6. D
104 = 10,000, indicating that you should move the decimal four places to
the right. So 0.123 × 104 = 0.123 × 10,000 = 1,230, choice (D).
7. A
Know your perfect squares.
choice (A).
and
. So
8. B
Given a diameter of 6, the radius must equal
of 6, or 3. Next, the
circumference (c) = 2πr = 2π(3) = 6π. The area (b) = πr2 = π(32) = 9π. Add
those two: 9π + 6π = 15π.
9. B
To find the probability of something occurring, divide the number of
desired outcomes by the number of total outcomes. In the example of
the bag of marbles, you begin with 8 + 4 + 7 + 5 = 24 marbles, and draw
out 8, leaving you with 16 marbles. Out of those 16 marbles, 4 must be
white since the chance of drawing a white marble is now
or
. If
you are le with 4 white marbles, you must have already withdrawn 4
white marbles. (B) is correct.
10. If B is equal to the number of books that Janice has, and you know that
Liza has 40 fewer than 3 times the number of books that Janice has, Liza
has 3B − 40 books, and Janice has B books. Together they have 4B − 40
books, choice (C).
11. D
The perimeter of a square is 4s where s is the length of a side. If a square
has a perimeter of 32, then it has a side length of 8. The area of the
square is s2 = 82 = 64, choice (D).
12. C
You can simplify this expression as follows:
Remember to subtract exponents when dividing.
13. C
Go through the answer choices one at a time, and select the choice
whose digits have a sum and product that are equal.
(A) 111. Product =
Sum = 1 + 1 + 1 = 3
(1)(1)(1) = 1
Eliminate.
(B) 220. Product =
(2)(2)(0) = 0
Sum = 2 + 2 + 0 = 4
Eliminate.
(C) 321. Product =
Sum = 3 + 2 + 1 = 6
(3)(2)(1) = 6
Choice (C) is correct.
14. D
If x =
, and we are asked to solve for y when
plugging in
for x.
, begin by
. Cross-multiply and solve.
y = 8, so y =
64, (D).
15. D
When parallel lines are crossed by a transversal, all acute angles formed
are equal, and all acute angles are supplementary to all obtuse angles.
So in this diagram, obtuse angle y is supplementary to the acute angle
of 55°. Angle x is an acute angle, so it is equal to 55°. Therefore, angle x is
supplementary to angle y, and the two must sum to 180°.
16. A
If you’re looking for a in terms of b, isolate the a on one side of the
equation.
3ab = 6
ab = 2
17. C
Distribute the numbers outside the parentheses and solve for y.
18. B
Since RS and RT are equal, the angles opposite them must be equal.
Therefore, angle T = angle S. Since the degree measures of the three
interior angles of a triangle sum to 180, 70 + angle measure S + angle
measure T = 180, and angle measure S + angle measure T = 110. Since
the two angles, S and T, are equal, each must have angle measures half
of 110, or 55.
19. B
When D is divided by 15, the result is 6 with a remainder of 2. That
means that D = 6(15) + 2 or 92. When 92 is divided by 6, the remainder is
2. (B) is correct.
20. C
The average of 7 consecutive even numbers is 24. In a set of evenly
spaced numbers, the median is the same as the average. That means
that 24 must be the middle number the set of numbers. So the set must
be {18, 20, 22, 24, 26, 28, 30}. The largest number is 30, choice (C).
21. D
The surface area of a rectangular solid is 2lw + 2lh + 2wh. In this case that
would be (2 × 2 × 3) + (2 × 2 × 4) + (2 × 3 × 4) = 12 + 16 + 24 = 52 square
inches, choice (D).
22. D
If 100 ÷ x = 10n, that can be rewritten as
. Cross-multiply
and you get 100 = 10nx. Divide both sides by 10 to solve for nx.
(A) is correct.
23. B
A circle contains 360°, so:
24. C
5! = 5 × 4 × 3 × 2 × 1 = 120
25. A
If Melissa has 5n photographs, and she gives n photographs to each of
three friends, she would have given away 3n photographs. 5n − 3n = 2n.
(A) is correct.
Answers and Explanations
PART 6: ELECTRONICS INFORMATION (EI)
1. B
Loads convert electrical energy into some other form of energy.
Examples of loads include heating elements (heat), light bulbs (light),
and solenoids (motion).
2. C
The choices represent four different diode symbols: (A) a zener diode,
(B) a tunnel diode, (C) a photosensitive diode, and (D) a light-emitting
diode (LED).
3. A
A hertz is a unit of measurement used to express the frequency (cycles
per second) of alternating current. One hertz (Hz) is the same as one
cycle per second. Choice (C) is incorrect because it indicates the rate of
change in frequency rather than the frequency itself.
4. B
A conductor is an element that freely conducts electricity, whereas an
insulator does not conduct electricity at all. A semiconductor is neither a
good conductor nor insulator, but has some remarkable properties that
make it very useful for making electronic components.
5. D
An earth ground is found outside a building, and normally utilizes
conductors such as conduit or pipe that is already in the ground. All of
the ground connectors in a residential wiring system will be attached to
an earth ground, which is used to “funnel” away stray electricity in
appliances and prevent it from causing electrical shock. A ground does
not measure resistance.
6. B
In electron flow theory, electrons flow away from areas of excess
negative charge to those with a deficiency of negative charge. When a
conductor is connected across the terminals of a battery, the electrons
in the conductor will be forced away from the negative terminal of the
battery and toward the positive terminal. Therefore (C) is clearly wrong.
Electrons can flow through solids and gases as well as liquids, so (A) is
incorrect. While resistance can reduce the flow of electrons, it does not
necessarily stop the flow completely, so (D) is incorrect.
7. A
Electrical pressure is known as voltage, and it is measured in volts
(symbolized by the letter V).
8. C
This is the circuit symbol for an ohmmeter, (C), which is used to measure
resistance.
9. B
This symbol represents a series-parallel circuit, which would have some
components, such as an on/off switch, wired in series with a number of
loads that are connected in parallel.
10. A
Ohm’s law tells us that V = I × R. If voltage stays constant, and resistance
R rises, current I would have to drop.
11. A
Ohm’s law tells us that R = V ÷ I. If resistance R stays constant, and
voltage V rises, current I will also have to increase.
12. A
Since V = I × R, and the current is the same across all the resistors, an
increase in resistance must result in an increase in the voltage drop.
13. B
A capacitor is made to block DC (direct current), but allow AC
(alternating current) to flow. Capacitive reactance is a capacitor’s
“opposition” to the flow of current, and this tends to diminish as the
frequency of alternating current increases.
14. D
The symbol for the transistor has an arrow that identifies the emitter.
The direction of the arrow tells us what type of transistor it is; this is a
PNP transistor.
15. D
An electromagnet’s magnetic field becomes stronger when more turns
of wire are added to it, more current is passed through the coil, or an
iron core is placed in the middle of the coil.
16. C
When current passes through a resistance, a voltage drop will take place.
This represents an energy loss, and this energy is normally dissipated in
the form of heat.
17. A
Ohm’s law states that voltage in volts is equal to the current in amperes
multiplied by the resistance in ohms, or V = I × R. V represents voltage,
and I represents current. Current is the rate of flow of electrons, or the
intensity of the flow. (Specifically, I is the rate of charge flow.) Finally, R
represents resistance.
18. B
When current flows freely through a diode, this is known as “forward
bias.” If the orientation of the diode is such that it blocks current flow,
that would be reverse bias. Open and grounded are irrelevant to the
question that was asked.
19. C
A transistor has three connections: the base, the emitter, and the
collector. The transistor is switched off and on by voltages applied to its
base. When a voltage appears across the base-emitter junction, the
transistor switches on and allows current to flow between the collector
and emitter.
20. A
For a simple parallel circuit with four resistors of equal value, divide the
resistance of a single component by the total number of components.
For this parallel circuit, you have four 1,000 ohm resistors, so 1,000 ohms
÷ 4 = 250 ohms.
Answers and Explanations
PART 7: AUTO AND SHOP INFORMATION (AS)
1. A
Soldering does not produce the electric arc that welding does. Welders
must cover all exposed skin with protective clothing and wear face
shields with light filters for protection.
2. A
The vast majority of drill bits are made to cut while rotating in a
clockwise direction (as viewed from above). These are known as right
hand drill bits. (Notice that choices (B) and (C) are logically equivalent
and therefore must be incorrect, as each question has only one correct
answer.)
3. A
A motor oil with a “C” prefix for its quality rating would be suited for
diesel engine use (i.e., a CD rating). Motor oil that had both an “S” and a
“C” rating would be suited for either gasoline or diesel engine use. An
example of this would be motor oil with a rating of SJ/CD.
4. B
Coil-on-plug ignition systems eliminate the need for spark plug wires
because the ignition coil is mounted directly over the spark plugs.
Secondary coil winding, (A), spark plugs, (C), and primary coil winding,
(D), are still necessary components in a coil-on-plug ignition system.
5. C
A double overhead cam arrangement puts two camsha s into each
cylinder head, and makes it so one cam operates the exhaust valves in
that head, and the other operates all the intake valves. Since the
configuration of a V-8 engine has two heads, there would be a total of
four camsha s.
6. C
This is a round rasp. Carpenters would use a round rasp for cleaning out
holes in wood. Round rasps are useful for cleaning up holes, whereas a
flat rasp would be used to smooth flat surfaces.
7. D
Using an oxyacetylene cutting torch involves the burning of oxygen and
acetylene to produce a flame that is hot enough to melt steel.
8. A
All automotive electrical systems are designed to utilize direct current
(DC). Some vehicles may use a negative ground as part of their electrical
systems, but not all cars do, so (C) is incorrect.
9. B
As the lead-acid battery discharges, the sulphuric acid in the electrolyte
is reduced to water. The lead plates then become lead sulphate.
Charging the battery restores the chemical composition of the lead
plates and the electrolyte.
10. A
The camsha is responsible for the -opening and closing of the engine’s
intake and exhaust valves. The camsha turns at one-half the speed of
the engine’s -cranksha .
11. A
An outside micrometer is used to measure the outside dimensions of
small things, such as cylinders, spheres, or relatively flat, thin objects.
12. D
The most common type of pliers is the combination slip-joint. These are
adjustable at the joint of the two handles of the pliers. With two
different positions to choose from, these pliers can grip objects in a wide
range of sizes.
13. C
A coping saw is used to make fine, curving cuts. This saw uses a thin,
flexible blade that is held tight on a wide frame.
14. D
The thermostat controls engine temperature by allowing coolant to flow
into the radiator when the coolant temperature rises above a certain
level.
15. A
Since the piston is moving downward and the intake valve is open, this
image depicts the intake stroke, which is the first stroke in the fourstroke cycle.
16. B
A specific mixture of air and fuel plus an ignition source to get the whole
thing going is required for combustion.
17. A
The firing order for four-cylinder engines is 1-3-4-2. Therefore, (A) is the
answer.
18. B
It takes two full revolutions of the cranksha to complete one cycle of
events in a four-stroke cycle engine. This means that all of the cylinders
in the engine must complete a power stroke in two revolutions of the
cranksha . So in one revolution, only three cylinders will fire. Thus, the
correct answer is (B).
19. C
Claw hammers are a more specialized tool o en preferred by
carpenters. Their purpose is twofold. The hammer head has two ends:
One drives nails and the other removes them. This is the tool least likely
to be found in a mechanic’s tool box.
20. B
Most solders are an alloy of lead and tin. The percentages of each metal
in the solder will vary depending on the desired properties of the solder,
i.e., melting point.
21. D
An automobile battery, or lead-acid battery, is made up of lead plates
immersed in an electrolyte made up of sulphuric acid and water.
22. A
Moving the ignition switch to the “start” position sends an electrical
current to the starter solenoid. This engages the starter drive gear onto
the engine’s ring gear, which is located on the flywheel.
23. A
Sockets come in both 6- and 12-point designs. Six-point is a stronger
design, and is usually the mechanic’s first choice in the smaller socket
drive sizes. However, 12-point is definitely the most popular in large
drive sizes.
24. C
The stoichiometric, or ideal, air-fuel ratio is 14.7:1. This means that 14.7
pounds of air is combined with 1 pound of fuel to create an ideal air-fuel
mix.
25. A
It is the brake rotor attached to the wheel that rotates. Then the brake
caliper clamps to slow the car wheels down. While a brake drum does
rotate with the wheel, it is not a component of a disc brake system.
Answers and Explanations
PART 8: MECHANICAL COMPREHENSION (MC)
1. A
Torque results in a twisting motion in an object. This is very different
from (B) horsepower (the rate that work is done), or force (either (C) a
push or pull, or (D) a force that travels in a circle).
2. B
Speed is different from velocity, in that velocity (which is a vector
quantity) implies both speed (a scalar quantity) and direction.
3. B
The relationship between force, mass, and acceleration is described
using the formula F = ma. If mass increases, more force is required to
achieve the same acceleration rate.
4. A
Force is a vector quantity. This means that it expresses both magnitude
and direction.
5. C
The definition of mechanical advantage is the advantage gained by the
use of a mechanism in transmitting force. For example, a lever and
fulcrum can be used to multiply the force applied to an object.
6. D
A hockey puck experiences kinetic friction (however small) that causes it
to lose velocity.
7. B
This is an example of meshed gears. Meshed gears always revolve in
opposite directions.
8. B
This is not a true statement because weight is dependent on both mass
and acceleration due to gravity (W = mg).
9. C
The coefficient of static friction is always greater than the coefficient of
kinetic friction. If a force is applied, but the box does not move, no work
has been done (W = Fd). The nature of the surface the box rests on will
define the coefficient of friction between the box and that surface.
10. A
The mechanical advantage of a wheel and axle system is determined by
the ratio of the radius of the wheel where the force is applied to the
radius of the wheel where the force is transferred. In this case, the ratio
of the radii is 10:2.5 or 4:1.
11. B
Three inches of movement multiplied by 20 pounds per inch is 60
pounds of force.
12. A
Torque (twisting force) can be increased by increasing the length of the
wrench, or by increasing the force applied to the wrench.
13. B
In accordance with Newton’s first law of motion, a vehicle traveling at a
constant speed has no net forces acting on it.
14. B
The outlet pipe on tower B is nearer to the bottom of the cistern than
the outlet pipe for tower A. Therefore, it will release more water than
tower A. While tower B will release water faster due to increased
pressure lower in the cistern, there is no way of knowing how much
faster from the information that is provided.
15. C
Because there are three cords holding sign B, they are under
the
tension of the cord holding sign A.
16. A
The illustration shows a first-class lever because the fulcrum is between
the load and the effort (force).
17. C
Accelerating at the rate of
will result in a velocity of
at the
end of ten seconds.
18. A
A wheelbarrow is an example of a second-class lever because the
fulcrum is at one end, the effort is at the other, and the load is in
between.
19. A
Gears that are an odd number away from the indicated gear move in the
opposite direction, while gears that are an even number away move in
the same direction as the indicated gear. In this case, gear Y is three
gears away from gear X, which means it will move in the opposite
direction as gear X. Gear X is moving clockwise, so gear Y must move
counterclockwise.
20. A
Using the formula W = Fd, it can be seen that 1 pound of force applied
through a distance of 1 foot will result in 1 foot-pound of work being
done.
21. B
The principle of conservation of energy tells us that the amount of
energy in the universe is constant.
22. D
Since there are 4 pulleys in the block and tackle shown, the mechanical
advantage is 4:1. Therefore, the rope must be pulled 4 times the
distance that the weight is raised, which is 4 × 2 = 8.
23. B
Choice (B) is not a true statement; the use of hydraulic force relies on the
fact that liquids are effectively incompressible.
24. C
A machine’s efficiency is expressed as the percentage of the source
energy that it converts into usable energy.
25. B
The velocity at which the ball travels will depend upon the impulse that
was applied to it. Impulse is determined by multiplying the force by the
amount of time that the force was applied. To increase the impulse, the
player should hit the ball with greater force and make contact with the
ball for a longer period of time.
Answers and Explanations
PART 9: ASSEMBLING OBJECTS (AO)
1. A
2. C
3. D
4. A
5. B
6. A
7. B
8. C
9. A
10. D
11. B
12. A
13. C
14. C
15. B
16. D
17. B
18. A
19. D
20. C
21. A
22. B
23. C
24. A
25. B
CHAPTER 3
WORD KNOWLEDGE
Know What to Expect
One of the subsections of the ASVAB evaluates your ability to identify the
meanings of words. This section, called the Word Knowledge (WK) section,
is essentially a test of your vocabulary. However, that’s not the entire story.
While knowing the definitions of many words will certainly help you in this
section, there are other ways to identify the correct answer and eliminate
the wrong answers in WK questions. This chapter will not only focus on
helping you improve your vocabulary, it will also help you develop
strategies to guess effectively when you may not know the meanings of the
words in the question.
On the WK section of the CAT-ASVAB, you will have 9 minutes to answer 15
vocabulary questions. If you are taking the paper-and-pencil ASVAB, you
will be given 11 minutes to complete a total of 35 questions. Whichever
version of the test you’re taking, your goal is the same: find the synonym
for a given word in a fraction of a minute.
A little more than half of the questions in the WK section will ask you to
define words with no context. We’ll call these No-Context WK questions.
Here’s an example of this type of question.
Gregarious most nearly means
(A)
(B)
(C)
(D)
conspicuous
twisting
outgoing
dark
If you happen to know the meaning of the underlined word, fantastic. If
not, don’t get discouraged. Although questions of this type do not provide
you with context clues, there are decoding strategies, or ways of guessing
a word’s meaning, that can help you answer these questions correctly.
Decoding strategies that involve understanding words’ prefixes, suffixes,
and roots will be a major emphasis of this chapter.
The other type of question you’re likely to see in this section will ask you to
define a word that appears in the context of a sentence. We’ll call these InContext WK questions. Take a look at an example of this type of question:
Nomadic tribes often move their villages when the
seasons change.
(A) warlike
(B) wandering
(C) exclusive
(D) hasty
Notice that in this type of WK question, you can use clues in the sentence to
help you find the word’s meaning. Later in this chapter, we’ll discuss ways
to get the most out of each sentence’s context to help you more effectively
predict the underlined word’s meaning. Oh, and don’t worry—we’ll be sure
to revisit the two questions above later in this chapter.
This chapter includes:
the Kaplan Method for Word Knowledge Questions
paraphrasing a word’s meaning
decoding strategies for guessing a word’s meaning, including:
prefixes, suffixes, and word roots
loose meaning associations
positive and negative charge
remembered context
using context to guess a word’s meaning
eliminating answer choices based on logic
strategies for building your vocabulary
practice questions
Regardless of the type of WK question you’re facing, having a consistent
and repeatable method will help you tremendously in this section. Use
Kaplan’s 3-Step Method for WK to attack every question you see in your
practice; by Test Day, it will be second nature.
The Kaplan Method For Word
Knowledge Questions
Learning Objectives
In this section, you’ll learn to:
apply the Kaplan Method for Word Knowledge questions
paraphrase the meaning of a word you are already familiar with
The sooner you learn and apply this method to your studies, the sooner it
can help you conquer the WK subtest.
THE KAPLAN METHOD FOR WORD KNOWLEDGE
QUESTIONS
Step 1:
Identify the word’s meaning, or apply decoding
Step 2:
Step 3:
strategies to guess its meaning.
Make a prediction.
Look for your prediction among the answer choices,
or strategically eliminate incorrect answers.
Let’s see how you’d apply that to a question in which you know the
meaning of the underlined word.
Question
The unusually cold weather was
an anomaly.
Analysis
Step 1: Anomaly means
“something unusual,” or
“something that doesn’t seem to
fit expectations.”
Step 2: Make a prediction before
looking at the choices: the
answer choice will mean “out of
the ordinary” or “unexpected.”
(A) oddity
Step 3: Correct. Oddity closely
matches that prediction.
(B) ally
An ally is a friend. Incorrect.
(C) anonymity
Anonymity is the state of not
being known. Incorrect.
(D) heat wave
A heat wave is not, by definition,
out of the ordinary. Also, in the
context of the sentence, a heat
wave does not make sense.
Incorrect.
Try one now on your own. Follow the method and try to make a prediction
if you can.
Bob shows excellent judgment in his choice of friends.
(A) dispensation
(B) wisdom
(C) jurist
(D) ability
Explanation
Your prediction may have differed but should have resembled the
following:
Step 1:
Judgment, the way it’s used in this sentence, means “the
Step 2:
ability to make good decisions.”
The answer choice will mean something like “discernment,”
Step 3:
or “good decision making.”
Only choice (B) matches that meaning: wisdom also means
“the ability to make good decisions.”
You’ll notice that Step 2 requires coming up with your own paraphrase of
what the answer choice will say. That can take some practice. So here’s a
chance to try it on your own. Use the following list of common words to
practice paraphrasing their meaning. If you don’t know what any of these
words mean, first look them up in a dictionary and then write down a
paraphrase in your own words. You can use casual language to describe
them if you like; you don’t have to sound like a dictionary when you’re
paraphrasing.
Word
Your Paraphrase
decision
__________________________________________
anxiety
__________________________________________
platform
__________________________________________
invention
__________________________________________
disgusting
__________________________________________
How easy did you find it to paraphrase the words’ meanings? It can take a
while to get the hang of paraphrasing, even when you know what a word
means, but it’s well worth it. Knowing what you’re looking for in the
answer choices will help you zero in on the answer much more efficiently
and accurately.
Your paraphrases may have varied; the following are sample answers using
casual, everyday language:
Word
Your Paraphrase
decision
choice
anxiety
nervousness, fear
platform
basis, thing that something is built on
invention
something new, or a lie
disgusting
nauseating, stomach-turning
Of course, there will be times when you will not know the underlined
word’s meaning. In those cases you’ll have to use decoding strategies or
context to make a guess about it. Let’s begin with decoding strategies.
Decoding Strategies For Guessing A
Word’s Meaning
Learning Objectives
In this section, you will learn to:
break apart words into prefix, suffix, and root
learn common prefixes, suffixes, and Greek and Latin word roots
guess at a word’s meaning using the word’s positive or negative
charge
You have many tools at your disposal for guessing a word’s meaning, and this
section will cover them each in turn.
BREAKING WORDS APART
One of the most effective decoding strategies is to break a word into parts. We
can do this because many long words in English are composed of a prefix (a
first
part that affects the word’s meaning) and/or a suffix (a final
part that can also affect the word’s meaning), plus a word root (a middle part
that o en derives from a Greek or Latin word).
For example, consider the word convolution. It breaks into parts like this:
con
+
volu
+
tion
prefix
+
word root
+
suffix
Suppose that you didn’t know what the word convolution means, but you did
know that the prefix con– means “together” and that the word root volu means
“turning” or “rolling.” The suffix –tion indicates that the word is a noun. So you
could guess that a convolution is something rolled up together. And that’s a
pretty good guess: In fact, convolution means a “coil or twist”
or “the act of coiling.” It can also refer to a complicated thought process that
might be described as “twisty.”
As a first step, get some practice breaking words apart into prefix, suffix, and
root. Be aware that not all the words below will have all of those parts. The first
one has been done for you.
Word
Prefix
Root
Suffix
dejection
de
ject
ion
Word
Prefix
Root
Suffix
paraphrase
___________________
___________________
___________________
multilingual
___________________
___________________
___________________
regenerate
___________________
___________________
___________________
ossify
___________________
___________________
___________________
Check your work against the answers below.
Word
Prefix
Root
Suffix
dejection
de
ject
ion
paraphrase
para
phrase
(none)
multilingual
multi
lingu
al
regenerate
re
gener
ate
ossify
(none)
oss
ify
So far so good, but what do all those word parts mean? Let’s start with the
meanings of common prefixes.
PREFIXES
There are many prefixes you might see on Test Day.
We offer a comprehensive list of prefixes in the Appendix of this book.
If you are struggling to raise your Word Knowledge score, we would encourage
you to make flashcards out of the word parts in the Appendix.
For our purposes here, we’re going to present a few prefixes to enable you to
get some practice working with them. Here are some extremely common
prefixes with examples:
Prefix
a, an
co,
col,
Meaning
not,
amoral: not related to morality; lacking regard for
without
morality atypical: not typical
together,
completely
collaborate: to work with another; cooperate
compatible: able to exist together with someone
com,
con
de
e, ex
in, im
pre
Examples
or something else; capable of harmonious
coexistence
away, off,
defame: to slander; to publicly speak ill of
down,
reversal
descend: to move from a higher to a lower place
out of,
efface: to rub or wipe out; surpass; eclipse
from,
former
exclude: to shut out; to leave out
not,
immoral: not moral; evil
without
impartial: unbiased; fair
before, in
front
premonition: a feeling that an event may happen
in the future
presentiment: foreboding
Prefix
pro
re
sub,
sup
Meaning
Examples
in front,
proceed: to go forward
before,
much, for
propound: to set forth for consideration
back,
recline: to lean back; to lie down
again
regain: to gain again; to take back
below,
under
subliminal: existing beneath consciousness
substandard: inadequate; below expectations or
requirements
Try your hand at working with prefixes. Use the list above to predict the
meaning of the following words:
Word
Your Prediction
preset
______________________________________________________________
subset
______________________________________________________________
reset
______________________________________________________________
The word root gno relates to knowing or discerning. Use that information and
the list of prefixes above to predict the meanings of the following words.
Word
Your Prediction
agnostic
______________________________________________________________
prognosis
______________________________________________________________
ignoramus
______________________________________________________________
The word root ject relates to throwing or throwing downward. Use that
information and the list of prefixes above to predict the meanings of the
following words.
Word
Your Prediction
eject
______________________________________________________________
dejected
______________________________________________________________
conjecture
______________________________________________________________
How did you do? Your answers may vary somewhat, but they should resemble
the definitions below.
Word
Your Prediction
preset
set before: that is, arranged beforehand
subset
something set under: that is, a small group within a larger group
reset
set again
agnostic
a without-knower: that is, a person that believes that the nature of God or the universe
is unknowable
prognosis
the act of knowing before: that is, a prediction about how a problem will progress
ignoramus
a not-knower: that is, a very ignorant person, an idiot
(formed by combining in + gno and then dropping the first n)
eject
throw out
dejected
thrown off or down: that is, sad, depressed
conjecture
something thrown together: that is, the formation of an opinion or guess without
enough information
Great work! The next step in decoding a long word involves looking at the end
of the word. That brings us to suffixes.
SUFFIXES
Unlike prefixes, suffixes usually do two jobs at once. They affect the meaning of
a word, and they also typically tell you what part of speech the word is. Here’s a
reminder about parts of speech:
PARTS OF SPEECH INDICATED BY SUFFIXES
Noun: a word that names a person, place, thing, or idea. For example,
the underlined words below are all nouns:
Hegel, a famous philosopher who lived in Germany, believed in an
idea called dialectic.
Verb: a word that expresses an action or state of being. Examples:
Julius constructed his own bookshelves.
I am normally a cheerful person.
Adjective: a word that modifies a noun. For example, the underlined
words below are all adjectives:
The quick brown fox jumps over the lazy dog.
Adverb: a word that modifies a verb, adjective, or another adverb. For
example, the underlined words below are all adverbs:
The second time he played poker, his skills were greatly improved
and he played his cards very carefully.
The other parts of speech are pronouns (he, she, it), interjections
(wow, ouch) , prepositions (of, to, in, on) , and conjunctions (but, nor,
for) . However, long words that end in suffixes don’t usually belong to
those parts of speech.
There are many
suffixes you might see on Test Day.
We offer a comprehensive list of suffixes in the Appendix of this book.
If you are struggling to raise your Word Knowledge score, we would encourage
you to make flashcards out of the word parts in the Appendix.
For our purposes here, we’re going to present a few suffixes to enable you to
get some practice working with them. Below is a list of some extremely
common suffixes with examples.
Suffix
Part of
Speech
It
Meaning
Examples
Usually
Indicates
able,
adjective
ible
ic
adjective
capable of,
changeable: able to be changed
worthy of
combustible: capable of catching fire
easily
having the
robotic: like a robot or having to do
quality of,
related to
with robots
melodic: having to do with melody;
sweetly musical
ion,
tion,
sion
noun
act of
doing, act
of being,
result of
action
notation: act or process of making
notes
sensation: act of feeling or
perceiving
ist
noun
one who
does an
action or
pianist: one who plays the piano
anesthetist: a medical professional
who administers anesthesia (that is,
has a trait
drugs that lessen pain or cause
unconsciousness)
state or
novelty: state of being new; a new
quality of
thing
solemnity: state of being solemn or
serious
ity
noun
Suffix
Part of
Speech
It
Meaning
Examples
Usually
Indicates
logy
noun
study of
geology: study of Earth’s structure
zoology: study of animals
oid
adjective
or noun
resembling
or almost
ovoid: resembling an egg, having an
oval or egg-like shape
asteroid: a small body orbiting the
Sun (literally, an almost-star)
ous
adjective
having the
bulbous: having a bulb-like shape
quality of,
having to
do with
venous: related to the veins
The word root am or amo relates to love or liking. Use that information and
your knowledge of suffixes to predict the parts of speech and the meanings of
the following words:
Word
Your Prediction: Part of Speech
Your Prediction: Meaning
amiable
_______________________________
_______________________________
amorous
_______________________________
_______________________________
amity
_______________________________
_______________________________
The word root anthro or andro means man or human. Use that information and
your knowledge of suffixes to predict the parts of speech and the meanings of
the following words:
Word
Your Prediction: Part of Speech
Your Prediction: Meaning
anthropology
_______________________________
_______________________________
anthropologist
_______________________________
_______________________________
anthropomorphize
_______________________________
_______________________________
android
_______________________________
_______________________________
misanthropic
_______________________________
_______________________________
How did you do? Your answers may have varied, but they should resemble the
definitions below.
Word
Your Prediction: Part of
Your Prediction: Meaning
Speech
amiable
adjective
capable of being liked or loved; likable
amorous
adjective
displaying love or attraction
amity
noun
liking, friendship
anthropology
noun
study of human beings
anthropologist
noun
one who studies human beings
anthropomorphize
verb
to make into something that resembles humans
android
noun
something (such as a robot) that resembles
humans
misanthropic
adjective
having a hatred of people (mis means bad,
wrong, or hateful)
Of course, prefixes and suffixes are only part of the story. You’ll also need to be
able to decode what’s in the middle of a word.
GREEK AND LATIN WORD ROOTS
Many, though not all, of the long words in English derive from Greek or Latin,
which means that learning some Greek and Latin word roots can help you
decode English words. In your practice with prefixes and suffixes, above, you
have already seen that a single word root can produce many words in English.
This section will examine a selection of word roots and how they form the basis
for English words. This discussion will be followed by in-format exercises
designed to help you put your decoding strategies to work.
There are many word roots you might see on Test Day.
We offer a comprehensive list of word roots in the Appendix of this book.
If you are struggling to raise your Word Knowledge score, we would encourage
you to make flashcards out of the word parts in the Appendix.
For our purposes here, we’re going to present a few word roots to enable you to
get some practice working with them. Below is a list of some extremely
common roots with examples.
Root
Meaning
Examples
Root
Meaning
Examples
ced, ceed,
cess
go, hold back,
yield
cessation: stoppage
incessant: continuous; without stopping
centr
center
central: in the center; important
concentrate: to bring to the center; to
direct to one point
pat, path
feeling,
suffering
empathy: identification with the feelings of
another
impassive: showing no feeling or emotion
vi, viv
life, living
vital: concerned with or necessary to life
PRACTICE WITH WORD ROOTS
Use your knowledge of prefixes and suffixes, along with the word root list
above, to predict the part of speech and meaning of the following words:
Word
Your Prediction: Part of
Your Prediction: Meaning
Speech
concentric
__________________________
__________________________________________
viable
__________________________
__________________________________________
__________________________
__________________________________________
conceded
Word
Your Prediction: Part of
Your Prediction: Meaning
Speech
procession
__________________________
__________________________________________
apathetic
__________________________
__________________________________________
pathology
__________________________
__________________________________________
vitality
__________________________
__________________________________________
eccentricity
__________________________
__________________________________________
How did you do? Your answers may have varied, but they should resemble the
definitions below.
Word
Your Prediction: Part of
Your Prediction: Meaning
Speech
concentric
adjective
together with the center: that is, having a common center
viable
adjective
able to live: possible or workable
conceded
verb
reluctantly accepted or gave up something
procession
noun
act of moving forward
apathetic
adjective
pathology
noun
study of suffering; study of diseases
vitality
noun
capacity for life or survival; state of being strong or full of
without feeling or emotion
life
eccentricity
noun
state of being out of the center: that is, oddity; state of
being odd or unusual
Full lists of word parts are in the back of this book, in the Appendix. Be sure
to get more practice with word parts before Test Day. The best way to do this
might be to read a variety of sources and, when you come across a long,
unfamiliar word, see if you can break it into parts and analyze the parts.
USING POSITIVE OR NEGATIVE CHARGE
One of the secrets to success in the WK section of the ASVAB is knowing that
you don’t actually need precise definitions of the words that are being tested.
As long as you can confidently eliminate three answer choices as being
incorrect, you’ll find your way to the correct answer. That means that many
times, just knowing if a word is positive, negative, or neutral will be enough to
answer the question correctly. For example, let’s return to a question you’ve
seen previously:
Gregarious most nearly means
(A) conspicuous
(B) twisting
(C) outgoing
(D) dark
Do you know what the word gregarious means? If so, then great, this is an easy
question for you. But let’s say you don’t know what it means. What do you do
then? Well, you can start by breaking the word down into parts, as you’ve seen
demonstrated earlier in the chapter.
But let’s imagine that you aren’t familiar with the root greg. While you may be
tempted to throw in the towel and give up, try something else: do you think
gregarious has a positive, negative, or neutral charge? If you’ve ever heard the
word gregarious used in conversation, then you probably heard it used to
describe a person. And was the person using the word gregarious delivering a
compliment or an insult?
Now, you may be thinking to yourself, “Hmm, okay, I don’t really know what
gregarious means, but I’m pretty sure I’ve heard it used to compliment
someone, so this is a positive word.” Now look through the answer choices.
Which of those, if applied to a person, would be considered positive? Three
answer choices are either negative or neutral. Only (C), outgoing, is positive
when applied to a person. Select it and move on.
Of course, using a word’s positive or negative charge should never be your first
strategy when tackling a WK question. Use this approach only when you have a
general but not specific understanding of the word.
(For the record, the root greg means “to flock to,” and the suffix -ious means “to
be full of.” Therefore, gregarious means “living with others, like a flock of
animals,” and the closest choice is (C) outgoing.)
Try this method out on a few words below. For each word you see, rate it as
positive, negative, or neutral.
Word
Positive, negative, or neutral?
diabolic
__________________________________________
harmony
__________________________________________
fanfare
__________________________________________
destitute
__________________________________________
burdensome
__________________________________________
Word
Positive, negative, or neutral?
zestful
__________________________________________
decision
__________________________________________
swampy
__________________________________________
currently
__________________________________________
Think about how you made the predictions you listed above. How did you
come to that determination? Was it because you recognized word parts or
remembered situations in which you’ve heard the word? Or was it more that
the word simply “sounded” positive or negative? Either one can work,
depending on how reliable your memory is. Now, take a look below. We’ve
included each word’s meaning, simply to confirm why it has a positive or
negative charge.
Word
Positive, negative, or
Meaning
neutral?
diabolic
negative
devilish or evil
harmony
positive
agreement, or a pleasing combination of tones in
music
fanfare
positive
song played in celebration, or advertisement
destitute
negative
poverty-stricken
burdensome
negative
very heavy; tiresome; troublesome
zestful
positive
full of enjoyment
decision
neutral
choice
swampy
negative
unpleasantly humid; resembling a swamp
currently
neutral
at the present time; now
USING REAL-WORLD CONTEXT TO GUESS AT A
WORD’S MEANING
One of the most common—and effective—ways of guessing a word’s meaning is
to place the word in context. Even if you may not know a textbook definition of
the word, perhaps you remember it being used in a specific phrase. Ask
yourself, “where have I heard this word before?” Sometimes, you will realize
that you did know the meaning of the word.
Take this question, for example:
Broach most nearly means
(A) poke
(B) introduce
(C) sermonize
(D) cook
Unfortunately, broach is one of those words that comes from Middle English, so
knowing Latin and Greek roots won’t be very helpful. And if you can’t rattle off
a specific definition of the word right away, you may think that this is a lost
point. But ask yourself if you have heard this word used in a common phrase
before. Does “broaching the subject” ring a bell? Perhaps you’ve heard a
parent, teacher, or television character use this phrase. Something along the
lines of: “Well, I didn’t want to talk about it, but Donny broached the subject
anyway.” Using the context of how the word is used in a phrase you’ve heard
before is a remarkable way to understand the “fuzzy definition” of a word. In
this example, broach would mean something like “bring up” or “start to
discuss.” The only word that is a close fit is answer choice (B), introduce.
Try this approach yourself. For each of the words below, try to place the word in
a common phrase that you may have heard before. How does the context of the
phrase help you determine the meaning of the word?
Word
Think of a phrase you’ve heard the word used in, and then use that to guess at the
meaning of the word:
vicarious
___________________________________________________________________________
jiffy
___________________________________________________________________________
guzzle
___________________________________________________________________________
hybrid
___________________________________________________________________________
Did those words sound familiar? When you tried to place them in phrases or a
real-world context, what did you come up with? Below, take a look at how a
person might have used common usage to help them determine the right
definition. Your answers, of course, may vary.
Word
Think of a phrase you’ve heard the word used in, and then use that to guess at the
meaning of the word (sample answers):
vicarious
“I’ve heard the phrase ‘So and so lived vicariously through someone else.’ I guess that
means vicariously is like experiencing something through someone else’s eyes.”
jiffy
“My dad used to say ‘I’ll be back in a jiffy.’ I guess a jiffy is really fast.”
guzzle
“I have a friend who is always talking about his truck being a real gas guzzler. He’s always
filling it up, so I guess being a guzzler means you consume a lot.”
hybrid
“There are a bunch of new cars out there that are considered to be hybrids because they
use a little bit of gas and a little bit of electric. Maybe hybrid means doing two things at
the same time.”
Notice that the predictions are not specific definitions or predictions that point
to the word’s meaning. Instead, the phrases allow you to form a fuzzy definition
of the word in your mind; that fuzzy definition will o en be more than enough
to select the right answer.
Making the Most of Context
Learning Objectives
In this section, you will learn to:
use the meaning of a sentence to predict an answer on InContext WK questions
use the meaning of a sentence to eliminate answer choices on
In-Context WK questions
In addition to the decoding strategies discussed above, you can also use
the sentence itself to help you answer In-Context WK questions. Context
simply means the words or phrases surrounding an underlined word, and
using context involves looking for clues in those other words in order to
help you guess at the underlined word’s meaning.
There are several ways context can be helpful. Sometimes the sentence
signals that the underlined word resembles another idea in the sentence.
Consider the following:
Question
Analysis
The children thronged around
the table like moths around a
flame.
The word like signals that,
whatever the children were
doing, they resembled moths
swarming around a flame. So
thronged must convey that same
sense.
Sure enough, thronged means swarmed or gathered in a crowd.
In each of the examples below, identify the word that tells you that the
underlined word is similar to some other idea in the sentence, and then
predict the meaning of the underlined word.
Sentence
The crowd greeted the
What word or words signal
Predict the underlined
similarity?
word’s meaning
_________________________
_________________________
_________________________
_________________________
_________________________
_________________________
famous chef with an
eagerness amounting to
fervor.
The budget meeting was a
difficult conversation;
indeed, it was almost a
quagmire.
Today’s creative child may
be tomorrow’s virtuoso.
Explanation
Your paraphrases may differ somewhat but should resemble the following:
Sentence
What word or
Predict the underlined
words signal
word’s meaning
similarity?
The crowd greeted the famous chef with
amounting to
tremendous enthusiasm
indeed
extremely difficult or
an eagerness amounting to fervor.
The budget meeting was a difficult
conversation; indeed, it was almost a
awkward situation
quagmire.
Today’s creative child may be
parallel drawn
someone very skilled at a
tomorrow’s virtuoso.
between today and
creative activity like art or
tomorrow
music
In other cases, sentences may contain words that signal that the
underlined word contrasts with or forms an unexpected combination with
another idea in the sentence. Consider the following example:
Question
Analysis
Question
Analysis
The best coaches are supportive
The word but tells you that
but exacting.
exacting either contrasts with
supportive or else that you would
not expect to see supportive and
exacting linked together. It is
unlikely that exacting is the direct
opposite of supportive, since the
writer of this sentence thinks
good coaches display both traits.
So it must be the case that
supportive and exacting are
somehow a surprising pair.
In fact, exacting means “making large demands.” Thus, the prediction
above is correct: while exacting does not mean the opposite of supportive,
it is perhaps a surprising idea to find linked with supportive.
In each of the examples below, identify the word that tells you that the
underlined word contrasts with or forms a surprising combination with
some other idea in the sentence, and then predict the meaning of the
underlined word.
Sentence
What word signals contrast or
Predict the underlined
an unexpected combination of
word’s meaning
ideas?
Sentence
What word signals contrast or
Predict the underlined
an unexpected combination of
word’s meaning
ideas?
Some human behavior is
_________________________
_________________________
_________________________
_________________________
_________________________
_________________________
learned, while other
human behavior is
instinctive.
Trisha found the task to
be enjoyable rather than
onerous.
I prefer action films but
had to sit through a
cloying love story last
Friday night.
Explanation
Your paraphrases may differ somewhat but should resemble the following:
Sentence
What word signals
Predict the underlined word’s
contrast or an
meaning
unexpected combination
of ideas?
Some human behavior is
while
learned, while other human
contrasts with learned, so
innate or inborn
behavior is instinctive.
Trisha found the task to be
enjoyable rather than
onerous.
rather
contrasts with enjoyable, so
tiresome or burdensome
Sentence
What word signals
Predict the underlined word’s
contrast or an
meaning
unexpected combination
of ideas?
I prefer action films but had to
but
contrasts with action films and
sit through a cloying love
has a negative charge, so too
story last Friday night.
sentimental or sugary
Sometimes context merely tells you whether an underlined word has a
negative or positive connotation. In many cases, this deduction may be
enough to answer the WK question. Consider the following example:
Question
Analysis
Jalisa was looking forward to a
Step 1: A respite must be a good
well-earned respite.
thing, because Jalisa is looking
forward to it. Also, the adjective
well-earned has a positive
connotation.
Step 2: Respite must be
something enjoyable or
beneficial.
(A) deadline
Step 3: Of the answer choices,
(B) incarceration
only (C) rest is likely to be
(C) rest
(D) prediction
enjoyable or beneficial. Choose
(C).
In fact, a respite is a period of rest or relief from work or from something
unpleasant.
Try it on your own. For each of the sentences below, identify the word or
words that signal whether the underlined word has a positive or negative
connotation. Then try, if possible, to predict the underlined word’s
meaning.
Sentence
What word or words signal that
Predict the underlined
the underlined word has a
word’s meaning
positive or negative
connotation?
I struggled to stay
_________________________
_________________________
_________________________
_________________________
_________________________
_________________________
awake as the
presentation droned
into evening.
Your injudicious
proposal would have
serious consequences
for our town’s future.
Wasting more money
on the -machine would
only exacerbate our
difficulties.
Explanation
Your paraphrases may have differed but should have resembled the
following:
Sentence
What word or words signal that the
Predict the
underlined word has a positive or
underlined
negative connotation?
word’s
meaning
I struggled to stay awake as the
struggled
continued in a
presentation droned into
boring or
evening.
monotonous
way
Your injudicious proposal would
serious consequences
unwise
wasting
worsen
have serious consequences for
our town’s future.
Wasting more money on the
machine would only exacerbate
our difficulties.
Finally, sometimes the context surrounding an underlined word’s meaning
simply defines that word or hints at its meaning. Remember this example
from the beginning of the chapter?
Question
Analysis
Nomadic tribes o en move their
villages when the seasons
Step 1: Whatever nomadic tribes
may be, they move around a
change.
good deal.
Step 2: Check the answer choices
for a word that means moving
around.
Question
(A) warlike
(B) wandering
Analysis
Step 3: (B) wandering matches
the prediction best.
(C) exclusive
(D) hasty
In fact, the sentence in the question above simply defines nomadic, which
means “moving from place to place; having no fixed dwelling-place.”
Try your hand at the following examples:
Sentence
Predict the meaning of the underlined word
As Lydia struggled to understand the difficult
_______________________________________
material, her bewilderment became obvious
to the teacher.
The thieves took pains to cover their tracks
_______________________________________
on the way to their clandestine meeting.
The incoming freshman found the Advanced
_______________________________________
Econometrics course material to be opaque.
Explanations
Your paraphrases may differ somewhat but should resemble the following.
Sentence
Predict the meaning of the underlined word
Sentence
Predict the meaning of the underlined word
As Lydia struggled to understand the
She struggled to understand, so bewilderment likely
difficult material, her bewilderment
means confusion or lack of understanding.
became obvious to the teacher.
The thieves took pains to cover their
The thieves were clearly trying to keep their
tracks on the way to their clandestine
meeting a secret, so clandestine likely means secret.
meeting.
The incoming freshman found the
Whatever Advanced Econometrics is, it sounds too
Advanced Econometrics course material
hard for a freshman. So the freshman likely found it
to be opaque.
to be very difficult to understand.
Of course, sometimes you will struggle to glean clues from the context of a
sentence. You may, in these cases, be able to eliminate some answer
choices by mentally replacing the underlined word with each of the answer
choices to try to “hear” which choices sound wrong. Study the following
example to learn how a test taker might go about this:
Question
Analysis
Everyone on the committee
agreed that acting with
Steps 1 and 2. The sentence
doesn’t give many hints aside
circumspection was important.
from suggesting that
circumspection is probably a
good thing.
Question
Analysis
(A) wisdom
(B) voting
Step 3. More than one of the
answer choices has a positive
(C) caution
(D) individuality
connotation. Try each in the
original sentence:
(A) Everyone on the committee
agreed that acting with wisdom
was important. That seems like
an odd thing to say. Isn’t wisdom
always important? Try the others.
(B) Everyone on the committee
agreed that acting with voting
was important. That doesn’t
seem to make much sense.
(C) Everyone on the committee
agreed that acting with caution
was important. That makes a
great deal of sense.
(D) Everyone on the committee
agreed that acting with
individuality was important. That
seems to go against the idea of a
committee, especially one where
everyone agrees.
Choice (C) is the best fit.
Not surprisingly, circumspection means “caution or the act of carefully
considering.”
Try your hand at the example below. If you are having trouble predicting
what the underlined word means, mentally reread the sentence,
substituting each answer choice, to find the one that sounds most
sensible.
Joanna feigned happiness at the wedding.
(A) created
(B) passed out
(C) pretended
(D) concealed
Explanation
Steps 1 and 2. Perhaps you had trouble applying decoding strategies or
using context here. If so, go directly to the choices.
Step 3. Try the answer choices one by one in the sentence:
(A) Joanna created happiness at the wedding. That doesn’t make a lot of
sense. Weddings might make people happy, but people don’t typically say
that one individual creates happiness.
(B) Joanna passed out happiness at the wedding. Unless happiness is a new
kind of party favor, this makes no sense. (This answer choice was probably
intended to tempt test takers who think feign looks like faint.)
(C) Joanna pretended happiness at the wedding. This makes sense: if
Joanna had some reason to be unhappy that day, she may have had to
pretend to be happy.
(D) Joanna concealed happiness at the wedding. Although it’s possible that
someone might have a reason to conceal, or hide, their happiness at a
wedding, that seems far less likely than choice (C).
Eliminating Answer Choices Based on
Logic
If you really can’t come up with a prediction, or if context is proving to be
no help, then you may in some cases be able to eliminate answer choices
by thinking logically about them. For example, if two answer choices mean
nearly the same thing, they must be wrong, since the ASVAB has only one
right answer for each question. Consider the following example:
Question
Analysis
Legerdemain most nearly means
Steps 1 and 2. Hard to see
recognizable prefixes, suffixes, or
word parts in this word. Also,
there’s no context. Difficult to
predict. Look at the choices.
Question
(A) monster
(B) massive amount
(C) magic trick
(D) ogre
Analysis
Step 3. Now, monster and ogre
are not exactly synonyms, but
they both mean creatures that
are frightening and dangerous.
Therefore it’s unlikely that either
of them are correct. Eliminate (A)
and (D).
At this point, either make a guess
between (B) and (C) or try to
remember situations in which
you’ve heard the word
legerdemain.
In fact, legerdemain means sleight of hand, so magic trick is the best fit.
If two answer choices have opposite meanings, it may be likely that one of
them is correct. That’s because test makers o en include an answer choice
that means the opposite of the correct answer. Study the following
example:
Question
Hauteur most nearly means
Analysis
Steps 1 and 2. Hard to see
recognizable prefixes, suffixes, or
word parts in this word. Also,
there’s no context. Difficult to
predict. Look at the choices.
Question
Analysis
(A) author
(B) arrogance
Step 3. Choices (B) and (D) have
opposite meanings, so it may be
(C) moisture
(D) humility
the case that one of them is
correct.
Once you have eliminated (A) and (C), you may have to simply guess
between the other two. Alternatively, if you happen to have a sense that
hauteur has a negative charge, you could use that to guess that it probably
means arrogance. You could also think about the fact that hauteur sounds
like haughty, which means arrogant. So (B) is indeed correct.
In conclusion, eliminating choices based on logic usually helps you to
narrow choices down to two. You may need to use another strategy or
simply guess in order to select from the remaining two choices.
Try to eliminate wrong answer choices using logic in the following
questions.
Demur most nearly means
(A) trust
(B) investigate
(C) believe
(D) disagree
Logy most nearly means
(A) oblong
(B) lively
(C) sluggish
(D) chubby
Explanations
1. Steps 1 and 2. Perhaps you don’t know the meaning of demur and are
having trouble applying decoding strategies to the word.
Step 3. Scan the choices. (A) trust and (C) believe are very similar in
meaning, and therefore it’s unlikely that one of them is correct. Eliminate
them.
Either guess between (B) and (D) or apply another strategy. It may be
helpful to note that the prefix de can mean away from, and the prefix dis
can mean not or opposed to. That may signal that these words are similar.
Choose (D) disagree. (In fact, to demur means “to raise objections,
disagree, or hesitate.”)
2. Steps 1 and 2. Perhaps you don’t know the meaning of logy and are
having trouble applying decoding strategies to the word.
Step 3. Scan the choices. (B) lively and (C) sluggish are opposites, so it may
be that one of them is correct. Either hazard a guess or try to remember if
you’ve heard logy anywhere. You may remember that it has a slightly
negative charge, which makes (C) a better fit. (In fact, logy means
“sluggish.”)
Strategies for Building Your
Vocabulary
You now have a variety of strategies for conquering the WK section of the
ASVAB. But those tips aren’t helpful if your vocabulary remains poor. To
learn more words between now and your ASVAB Test Day, make this
commitment: learn seven new words a day. If that sounds like too few,
rest assured, it’s plenty—in fact, that’s nearly 50 words a week.
The best and most efficient way to improve your vocabulary is to
consume as many books, magazines, and newspapers that you can get
your hands on. The reason for this is pretty straightforward: learning
words in context, as you read, helps you retain those words longer and
with greater precision than learning those words by themselves, with no
context. If you have a smartphone, download a dictionary app and look up
any words that you don’t know. If you’re at your computer, simply use a
search engine. Always look up unfamiliar words that you encounter in your
reading of books and magazines, as well as words you see on the Internet,
hear in movies, or encounter in daily conversation.
Another tried and true method for improving your vocabulary is to make
and use vocabulary flashcards. While the “making” part of flashcards is
o en overlooked, its value is significant—the act of writing a word and its
definition on an index card will help you remember that word’s definition
both as a visual image and as an action. So, here’s your task: as you
encounter and learn new words, write them down on index cards and, as
soon as you’re able, write the definitions of those words on the backs of
the cards. Then, when you have some spare time, browse through your
pile. Once you feel like you’ve really “got” a word, and that you won’t lose
its definition, remove it from the pile. If you follow through with this
method, you’ll find that you’re constantly adding and removing words
from your pile of vocabulary cards.
Some folks find that creating a vocabulary notebook is more convenient
than flashcards. The idea is similar: jot down words you don’t know as you
find them in your readings and daily interactions, and look up their
definitions. List words in the le -hand column and their meanings in the
right-hand column. Cover up or fold over the page to test yourself. See how
many words you can define from memory.
Finally, there are a number of apps and websites you might use to
improve your vocabulary. To find out about Kaplan vocabulary apps, call 1800-KAPTEST or visit your virtual app store.
A er you learn new words, try to use them in conversation. This is an
excellent way to confirm that you truly understand a word’s meaning and
the proper context in which to use it. If you have an ASVAB study partner,
try to have a conversation in which each person must use an ASVAB
vocabulary word in a sentence. You’ll be surprised by how well the words’
definitions “stick” once you’ve correctly used them in conversation.
ASVAB TIPS
Improve your vocabulary by:
reading books, magazines, newspapers, and articles on the
Internet
looking up words you don’t know and jotting down their
definitions either:
on flashcards or
in a vocabulary notebook
making use of vocabulary-building websites or apps
committing to learning seven words every day
using recently learned words in daily conversation
WORD KNOWLEDGE PRACTICE SET 1
For each question, select the answer choice that most closely
matches the meaning of the underlined word. This question set
has 15 practice questions, which is the number of Word
Knowledge questions you will see if you take the CAT-ASVAB.
1. Ghastly most nearly means
(A)
(B)
(C)
(D)
fun
lazy
torrid
awful
2. The brothers ran away in cowardice.
(A) pain
(B) fear
(C) hopelessness
(D) temperance
3. Resignation most nearly means
(A)
(B)
(C)
(D)
losing
waste
acceptance
pride
4. She promised to cooperate with the authorities.
(A) fight
(B) talk
(C) work with
(D) placate
5. Everyone says he lost the election due to lack of initiative.
(A) satisfaction
(B) irritation
(C) money
(D) ambition
6. The city council sought reparations for the oil spill.
(A) compensation
(B) sadness
(C) thanks
(D) antipathy
7. Many times, the older sibling holds dominion over her younger
siblings.
(A) authority
(B) safety
(C) ability
(D) guilt
8. The professor did his best to appear universally erudite, even
when asked questions about subjects he knew little about.
(A) civil
(B) progressive
(C) scholarly
(D) amoral
9. Tangible most nearly means
(A) real
(B) open
(C) graphic
(D) costly
10. Alleviate most nearly means
(A) elevate
(B) improve
(C) encompass
(D) make foreign
11. Trite most nearly means
(A) snug
(B) correct
(C) modern
(D) stale
12. Imitating a marching band, the children used pots and pans to
make a loud clamor.
(A) noise
(B) protest
(C) music
(D) harmony
13. Candid most nearly means
(A) able
(B) whimsical
(C) valid
(D) honest
14. A er careful study, he was able to discern which model would be
the best car for his needs.
(A) avoid
(B) spoil
(C) perceive
(D) savor
15. Dupe most nearly means
(A) double
(B) delay
(C) deceive
(D) delight
WORD KNOWLEDGE PRACTICE SET 2
For each question, select the answer choice that most closely
matches the meaning of the underlined word. This question set
has 15 practice questions, which is the number of Word
Knowledge questions you will see if you take the CAT-ASVAB.
1. The athlete trained for the competition with vigor.
(A) stiffness
(B) intensity
(C) swelling
(D) concern
2. Enigma most nearly means
(A) puzzle
(B) motor
(C) energy
(D) clarity
3. She displayed fortitude in finishing the race despite the pain in
her foot.
(A) speed
(B) cheerfulness
(C) courage
(D) vulnerability
4. The frugal man was always reluctant to spend money.
(A) fearful
(B) thri y
(C) imprudent
(D) lavish
5. Finding just the right part for her old car at the swap meet was
fortuitous.
(A) expected
(B) interesting
(C) lucky
(D) exciting
6. By his third fall, Jack’s enthusiasm for roller skating had abated.
(A) waned
(B) solidified
(C) renewed
(D) flourished
7. Congeniality most nearly means
(A) agreeability
(B) coldness
(C) competence
(D) beauty
8. His brusque responses discouraged further questions from the
students.
(A) amusing
(B) curt
(C) empathetic
(D) articulate
9. Eminence most nearly means
(A) mischief
(B) devotion
(C) greatness
(D) dishonor
10. The unwitting clerk was absolved when her manager confessed to
embezzling the money.
(A) impressed
(B) accused
(C) incarcerated
(D) exonerated
11. Disdain most nearly means
(A) sympathy
(B) dishonesty
(C) contempt
(D) flattery
12. Abnegate most nearly means
(A) approve
(B) hope
(C) deny
(D) recognize
13. Although she was not exactly friendly, she treated us with civility.
(A) honesty
(B) courtesy
(C) compliance
(D) rudeness
14. Deranged most nearly means
(A) unapologetic
(B) tamed
(C) relocated
(D) crazy
15. Although he never accused her outright, he insinuated that she
had lied about the incident.
(A) implied
(B) insisted
(C) concealed
(D) disavowed
Answers and Explanations
WORD KNOWLEDGE PRACTICE SET 1
1. D
Even if you didn’t know that ghastly means “awful,” if you had a sense
that ghastly has a negative charge, you could have gotten the correct
answer that way. Torrid, by the way, means hot or passionate, as in a
“torrid love affair.”
2. B
Context is useful here: the brothers ran away, so ask yourself what
might make someone run away. While pain and hopelessness are both
bad things, fear is far more likely to produce the response of running
away.
3. C
The suffix –ation tells you that this is a noun made out of a verb. The
verb here is resign. A good strategy at this point might be to remember
the contexts in which you’ve heard the word resign in life: people
resign from their jobs, but none of the answer choices convey that
sense. You may also have heard people say that someone was resigned
to his fate. That means the person had accepted his fate. So the noun
form, resignation, means acceptance.
4. C
This is a good candidate for using word roots: co– means with and
operate means work.
5. D
A good strategy here might be to mentally reread the sentence,
substituting each of the choices in turn. Choices (A) and (B) make no
sense in the context of this sentence. So now you’re le with (C) and
(D). Think about what words initiative sounds like: initial and initiate
might come to mind. They both have to do with starting things. That
doesn’t seem to have much to do with money, so eliminate (C). In fact,
initiative means “resourcefulness” or “drive,” so ambition is the best
match. (You could say that someone who has initiative or ambition is a
self-starter; hence the link with initial.)
6. A
Try decoding this one using word parts: Re– means “back” or “again.”
The root par means “equal,” and the suffix –ation tells you that the
word is a noun that describes the act of doing something. So
reparation means something like “the act of making something equal
again” or perhaps the act of making something right. Thus, choice (A)
compensation is the best match. In fact, reparations means
“repayment for loss suffered.”
7. A
An excellent strategy here would be to predict a meaning based on the
context of the sentence. What might an older sibling do to younger
siblings? Perhaps she would influence them or even boss them
around. Indeed, dominion means “control,” “sway,” or “authority.” (You
could also have used word parts here: dom relates to ruling or
authority.)
8. C
The professor wants to appear erudite even when he doesn't know
much about a subject. You can predict from the context that erudite
means “learned.” Choice (C) scholarly means “learned” and is the
correct answer. Civil, progressive, and amoral don't relate to knowing a
lot about a certain subject.
9. A
You might be able to remember other circumstances in which you’ve
heard the word tangible. And from those, you might have a sense that
something tangible can be felt or seen. From that, you should be able
to pick (A) real as the closest match. You could also use word roots
here: the root tang or tac relates to touch; something tangible is
touchable or real.
10. B
You may have heard the word alleviate in the context of “alleviating
pain,” meaning to make the pain less and help someone feel better.
Alleviate is a positive word that means “to ease or allay a bad
situation,” so the correct answer here is (B) improve. Elevate means “to
raise” (think elevator), and encompass means “to surround.”
11. D
If something is trite, it has been used or done so many times that it is
no longer fresh or original. For example, you might say that your
friend’s story about being stuck in an elevator was funny the first
hundred times she told it but is now trite. The correct answer is (D)
stale.
12. A
Use context to predict an answer: what are children likely to make with
pots and pans? Probably a loud, unpleasant noise. (B) protest is not
supported by the context of the sentence. And choices (C) and (D) both
have far too positive a connotation. It is unlikely the children produced
pleasant music or harmony.
13. D
This question is a good candidate for loose meaning associations.
Candid comes from the noun candor, which means “honesty.” Candid
means “sincere” or (D) honest. Although candid might sound a little
like “can do,” it does not mean (A) able. Choice (C), valid, is another
positive word that relates to truth, so it might have been tempting
here, but valid relates to facts or logic whereas candid and honest refer
to people. Choice (B), whimsical, means “playful” or “not serious”; if
you buy a new phone on a whim, you purchase it impulsively.
14. C
Use the context to make a prediction: study gives a person more
information, and more information allows that person to make better
choices. So a er study, he was able to see or decide which car to
choose. This matches choice (C), perceive You could also mentally
reread the sentence, substituting each answer choice. He is unlikely to
want to (A) avoid or (B) spoil the best car. He might (D) savor, or
“enjoy,” his car a er picking it out, but this sentence does not concern
what happens a er he finds a good vehicle.
15. C
You may have a sense that dupe has a negative charge. If so, you can
eliminate (A) double, which is neither negative nor positive, and (D)
delight, which has a strong positive charge. In fact, to dupe someone is
to cheat or lie to that person, and (C) deceive matches that meaning.
Related words are betray, delude, and dissimulate. Dupe can also be a
noun, meaning “someone who is easily taken advantage of.” You don’t
want to be someone’s dupe!
WORD KNOWLEDGE PRACTICE SET 2
1. B
Use context to predict the meaning of this word. An athlete will work
hard to prepare for a competition, and vigor means “strength,” “force,”
or (B) intensity. The athlete may feel concerned about the competition,
but the underlined word here deals with the athlete’s training, not his
feelings. If you thought the underlined word was rigor, you might have
picked (A) stiffness: be sure to read carefully.
2. A
An enigma is a mystery or (A) puzzle. You may have heard of the
Enigma machine, which was a famous encryption device used by the
Germans in World War II.
3. C
Because she finished the race even though she was in pain, you know
she was pretty tough. This aligns with her showing (C) courage. If
anything, a sore foot implies that she ran more slowly than usual, so
speed doesn’t fit. You don’t know whether she showed (B) cheerfulness
or was gritting her teeth with every step. Choice (D) vulnerability, or
“weakness,” is the opposite of what you need here.
4. B
On this question, the sentence actually defines the word for you.
Someone who is frugal avoids spending money; in other words, he’s
(B) thri y. Choice (A) fearful is too strong; you don’t know that he is
actually afraid to spend money, just that he’s not eager to do so.
Choice (C) imprudent means “not careful,” and is the opposite of the
correct answer. Choice (D) lavish means “very generous” or
“abundant” and is also the opposite of frugal.
5. C
The word fortuitous has the same root as fortune and fortunate, and it
means “based on luck”. The clue that the find was (C) lucky is the fact
that “just the right part” was found at a swap meet, where one may
encounter a random assortment of items and not necessarily those
one desires. Choice (A) expected is the opposite of the author’s
meaning. While the find may have been (B) interesting and (D) exciting,
these choices do not fit the root fortu, which conveys luck.
6. A
A er Jack had fallen several times, his enthusiasm was bound to be
less, not more. The words abated and (A) waned both mean
“lessened.” If you were not sure of the word waned, you might have
noticed that two of the other choices— (C) renewed and (D) flourished
—suggest more enthusiasm, not less. Choice (B), solidified, means
“made solid or firm.” All of these are the opposite of the meaning
needed here.
7. A
The prefix con– means “together,” so the word congeniality is likely to
indicate people or things coming together. This alone might lead you
to eliminate (B) coldness, meaning “lack of warmth” or
“unfriendliness.” Choice (C) competence and (D) beauty are both
positive characteristics but do not relate to coming together. However,
(A) agreeability suggests two people getting along. Thus, the prefix
alone could help you to strategically eliminate three choices and arrive
at (A) as the correct answer. In fact, the root word genial means “warm
and friendly.”
8. B
The clue in the sentence is that the students’ questions were
discouraged by his remarks. This tells you that the responses were not
helpful and perhaps even rude. This eliminates (A) amusing (funny)
and (D) articulate (spoken clearly) as answers. Choice (C) empathetic
means “sharing feelings”; the root path– connotes feelings, as in
sympathy (feeling for) and apathy (without feeling). Empathetic replies
would not discourage students. So you are le with (B) curt as the
correct answer, meaning “short and unresponsive.”
9. C
The word eminence is o en used as a title of respect for leaders,
especially religious leaders, and is used to honor a person of very high
rank or great distinction. As such, it can best be understood as
meaning (C) greatness. Choice (A) mischief and choice (D) dishonor
contradict the positive connotation of the word. Choice (B) devotion
might be tempting if you are familiar with the word’s frequent
association with religious leaders; however, the word eminence
describes the high rank of the individual, not the strength of belief.
10. D
The clue word unwitting tells you that the clerk was unaware of the
embezzlement. Also, it makes sense that when the manager confessed
to the crime, the clerk was found to be innocent. This is the meaning of
absolved and its synonym (D) exonerated. If you were unsure of the
meaning of exonerated, you could eliminate (B) accused because it is
the opposite of what is needed here. Likewise, (C) incarcerated—
meaning “jailed”—would give the sentence the opposite meaning.
Choice (A) impressed simply does not fit the context of the sentence.
11. C
The prefix dis– gives this word a clear negative connotation, allowing
you to eliminate (A) sympathy. And although (D) flattery is o en used
in a negative context, it is not an inherently negative word, so it can be
eliminated. While it is true that (B) dishonesty is negative, the word
disdain has no association with a lack of honesty. Disdain suggests
simply a negative judgment, and this is the meaning of (C) contempt.
12. C
The root word negate within abnegate means “to deny the existence of
something.” The prefix ab– means “away from,” so to abnegate means
“to turn one’s back on or reject.” This makes choice (C), deny, the
correct answer.
13. B
The contrast clue although tells you that the word civility has a
meaning opposite to “not exactly friendly.” So look for an answer
choice that says she was not unfriendly. Choice (B) courtesy means
“politeness,” which is consistent with an absence of unfriendliness.
Choice (A) honesty is not related to the clue about friendliness. Choice
(C) compliance means “obedience” and is also not related to
friendliness. Choice (D) rudeness is the opposite of the needed
meaning.
14. D
The prefix de–, meaning not, gives the word a negative connotation
and allows you to rule out the neutral words (C) relocated and (B)
tamed with some confidence. Another form of the word deranged is
disarranged, meaning “disordered.” Deranged can be used to describe
a person with a disordered mind, making (D) crazy an appropriate
synonym.
15. A
The contrast word although tells you that even though he did not
accuse her outright, or directly, he did accuse her. So the word
insinuated must mean that he accused her indirectly, and (A) implied
means “stated indirectly.” Choice (B) insisted would mean that he
made his accusation forcefully, which is the opposite of what he did.
Choice (C) concealed means “hid.” This is incorrect because he did not
hide or cover up her lie; instead, he accused her of lying. Choice (D)
disavowed means “denied or rejected,” which again contradicts the
fact that he did accuse her.
REVIEW AND REFLECT
As you review your work on these practice questions, ask yourself some
questions:
Did you remember to apply strategies, such as using word parts or
using real-life remembered context?
How o en were you able to sense whether a word had a positive or
negative charge?
How well did you use context on the In-Context questions?
Use your thoughts about these questions to guide your review of this
chapter.
Want more instruction and practice with Word Knowledge? Log in at
kaptest.com/login to watch the video in this book's online resources and
try more questions in the Qbank.
CHAPTER 4
PARAGRAPH COMPREHENSION
Know What to Expect
The ASVAB includes a reading section among its several subtests. This
section, called the Paragraph Comprehension (PC) section, presents short
passages for you to read and then asks questions based on those passages.
While the subject matter of each passage will vary, no outside knowledge is
required to answer the questions correctly. For each question in this
section, everything you need to answer the question will be contained in
the passage above it.
On the paper-and-pencil version of the ASVAB, the PC section will ask 15
questions about 13 or 14 short passages. Timing is extremely important in
this version of the test, as you are only given 13 minutes to answer these 15
questions. On the CAT-ASVAB, you are given 27 minutes to answer 10
questions. The extra time allows for the fact that question difficulty can
increase as you accumulate correct answers.
The Kaplan Method for Paragraph
Comprehension Questions
Learning Objective
In this section, you’ll learn to:
apply the Kaplan Method for Paragraph Comprehension
Questions
To be successful in both the paper and pencil and CAT versions of the PC
subtest, you will need to read the passages in an effective and efficient
manner. Keep in mind that your goal in this section is not to learn the
subject matter of the passages but simply to answer the questions
correctly. Therefore, your focus should be on understanding each
question’s task rather than absorbing every detail in the passage. In this
chapter, you’ll learn how to use Kaplan’s approach to PC questions to help
you answer each type of question you’ll see on the PC subtest.
Having a consistent and repeatable method will help you quickly and
confidently answer questions in this section. Use Kaplan’s 4-Step Method
for Paragraph Comprehension Questions to attack every question you see
in your practice and on Test Day.
THE KAPLAN METHOD FOR PARAGRAPH
COMPREHENSION QUESTIONS
Step 1:
Step 2:
Step 3:
Step 4:
Read the question stem to identify your task.
Read the passage strategically.
Make a prediction.
Find the correct answer.
STEP 1: READ THE QUESTION STEM TO IDENTIFY
YOUR TASK.
How you read and analyze a passage will vary depending upon the task
defined by the question stem, so it’s important to always read the question
before you look at the passage. A er you read the question stem and
identify the specific type of question you’re being asked, it’s time to read
the passage strategically. In this chapter, we will cover all the different
types of questions you might see on Test Day.
STEP 2: READ THE PASSAGE STRATEGICALLY.
Once you know your task, read as much of the passage as necessary to
answer the question. In a question that asks you to identify the main idea
of a passage, separate supporting details from opinions and
recommendations to determine the author’s overall point. Other PC
questions may ask you to identify specific details, or to determine the
meaning of a word. The key in this step is to read the passage in the way
that is appropriate to answer the specific question that is being asked.
STEP 3: MAKE A PREDICTION.
As mentioned earlier, every question in this section can be answered by
the information in the passage that precedes it; no outside information is
necessary. For each question, take a few seconds to predict what the
correct answer will look like. Sometimes you’ll know the answer without
even looking at the answer choices. Other times, you’ll have only a general
idea of the phrasing of the correct answer. Either way, taking the time to
predict will make it easier to find the correct answer.
STEP 4: FIND THE CORRECT ANSWER.
Once you come up with a prediction of the correct answer, simply find the
answer choice that is the closest match. If you are unable to make a
prediction, you’ll still have an opportunity to find the correct answer by
eliminating answer choices that you know are incorrect. Many will be
incorrect because they stray beyond the scope of the subject matter in the
passage. Other answer choices are incorrect because they are too extreme,
or they distort details in the passage. A er you’ve eliminated the wrong
answer choices, select the one that remains and move on to the next
question.
Conquering Paragraph
Comprehension Questions
Learning Objectives
In this section, you’ll learn to:
identify PC question types
read PC passages strategically
make accurate predictions
match your prediction to the correct answer
Global Questions
A common question type in the PC section is one that asks you to identify a
passage’s main idea or theme, the author’s purpose, or the tone of the
passage. Here’s what a Global question stem might look like:
Which of the following is the main idea of the passage?
The author’s tone in the passage above can be characterized as
The purpose of the passage above is to
The passage above is primarily concerned with
In order to find the main idea in a passage, you must be able to distinguish
the values an author assigns to different statements. In each passage that
asks you to determine a main idea, the author will use supporting details
to establish a main idea. Things like simple facts, other people’s opinions,
and background information can all operate as supporting details in a
passage. Those details are then used to support an author’s claim, which
o en comes in the form of a strong opinion, a recommendation, a
prediction, or a rebuttal to another person’s position.
As an example, imagine a passage with the following main idea:
“Purchasing gold is a wise investment.” This claim is not a fact but rather a
recommendation. In turn, the author needs to support this claim by
offering reasons why gold is such a good investment. Perhaps it’s because
“the amount of gold available worldwide is set to plateau,” or maybe it’s
because “gold is the worldwide monetary standard.” Those two
statements, alone or together, help to explain why gold would make a wise
investment. But the recommendation that gold is a good investment does
not explain why gold is the worldwide monetary standard.
So, one method for separating the main idea from the rest of the passage is
to realize that the supporting details and the main idea answer two
different types of questions, as you can see:
This:
Answers the question:
Main idea
What does the author believe?
Supporting details
Why does the author believe what he or she believes?
Sometimes, like when the author expresses a strong opinion, the main idea
will be clear. Words and phrases like thus, therefore, I suggest, and I believe
all indicate that the author is providing a strong conclusion. Other times, a
passage’s main idea will be more difficult to identify. In those passages, be
prepared to work a little harder to separate supporting ideas from the main
idea. O en, one of the tricks to zeroing in on the main idea of a passage is
to pay attention to structural clues that indicate a contrast. Words such as
but, though, however, although, and yet provide subtle clues into an
author’s point of view: the statement a er the contrast word is frequently a
reflection of the author’s opinion, especially in passages where the author
disagrees with someone else’s opinion.
Finally, on Global questions it is o en easy to eliminate a few answer
choices immediately. Wrong answer choices for Global questions usually
do one of the following:
They’re too specific, dealing with just one small detail of the passage.
They’re too general, going beyond the scope of the passage.
They’re contradictory to the information presented in the passage.
They’re too extreme; that is, they distort the author’s opinion by
overstating it.
Below, take a look at how a Kaplan-trained test taker approaches a typical
Paragraph Comprehension Global question. Remember to start with the
question stem, labeled with “Step 1” below.
Question
Analysis
Many countries around the world
Step 2: The passage starts with
have instituted laws that
background information that
mandate phasing out the use of
describes what countries are
incandescent light bulbs and
replacing them with alternative
doing about light bulbs. Then a
possible conflict is introduced:
light sources that consume less
the new type of bulb contains
energy. However, many
mercury, which is toxic. More
incandescent bulbs have been
replaced with fluorescent lights
background information is
provided: some governments are
containing the extremely toxic
pushing to add ethanol to
element, mercury. Similarly,
gasoline. The fourth and fi h
some governments have required
gasoline for automobiles to
sentences introduce a possible
drawback to the proposed
contain ethanol, a fuel that
change: using corn for fuel uses a
generates less pollutants than
lot of energy.
gasoline when burned. However,
ethanol is produced from crops
such as corn. Cultivating the
crops and converting them to
ethanol require large amounts of
energy, and the former also
increases the use of fertilizers,
which can leach into streams and
rivers.
Question
Analysis
The main theme of the passage is
that
Step 1: This is a Global question.
Read the passage to determine
the author’s main point.
Step 3: The author discusses two
things governments are trying to
do to reduce energy and
pollutants. A er each example,
she uses the contrast keyword
“however” to highlight the fact
that there are drawbacks to these
plans. That’s a solid prediction.
(A) environmental regulations
Step 4: Correct. This matches the
can have negative consequences
prediction.
(B) light bulbs and ethanol
Just because the regulations
regulations are misguided
have some drawbacks does not
mean they are necessarily
misguided. Incorrect.
(C) environmental concerns
This is an irrelevant comparison
should take precedence over
economic issues
between two considerations that
are not explicitly discussed in the
passage.
Question
Analysis
(D) fluorescent lights contain
While this is a valid inference that
more mercury than incandescent
can be made from the passage,
lights
this detail is not the main theme
of the passage.
Notice that the well-trained test taker follows a specific method. She is not
in a rush and takes her time in Step 3. She knows that a well-phrased
prediction will help her answer the question efficiently and confidently.
Now it’s your turn. Follow the Kaplan Method for PC by working through
each step deliberately. Focus on reading the passage strategically and
making a strong prediction. When you’re finished, check your work against
the explanation below.
Alchemy is the name given to the attempt to change
lead, copper, and other metals into silver or gold.
Today alchemy is regarded as a pseudoscience. It is
associated with astrology and the occult in the modern
mind, and the alchemist is viewed in retrospect as a
charlatan obsessed with dreams of impossible wealth.
But for many centuries, alchemy was a respected art.
In the search for the elusive secret to making gold,
alchemists helped to develop many of the apparatuses
and procedures used in laboratories today, and the
results of their experiments laid the basic conceptual
basis for the modern science of chemistry.
The central point of the passage is that
(A) alchemy is a pseudoscience
(B) alchemists tried, but failed, to make gold from
other metals
(C) many alchemists dreamt of becoming rich
(D) modern chemistry evolved out of alchemy
Explanation
Step 1: This Global question asks for the passage’s central point, or main
idea.
Step 2: The first sentence defines the topic of the passage: alchemy. The
second and third sentences state that alchemy is no longer recognized as a
real science; an analogy is drawn to astrology and the occult. The author
then uses the keyword “but” to draw a contrast: for a long time, alchemy
was a respected art. The passage then finishes by describing all of the
things that alchemists did that helped pave the way for modern chemists.
Step 3: There is no clear opinion from the author, but she does indicate
contrast in the middle of the passage. Focus on what the author discusses
a er the contrast: alchemy used to be a respected art, and the work of
alchemists laid the foundation for modern chemistry.
Step 4: Answer choice (D) matches the prediction that “the work of
alchemists laid the foundation for modern chemistry.” The other answer
choices don’t match the prediction, so eliminate them.
ASVAB STRATEGY
To correctly answer Global questions:
Identify any opinions, recommendations, suggestions, or
predictions made by the author.
Look to contrast words to help separate supporting details from
the author’s view.
Always make a prediction before looking at the answer choices.
Detail Questions
Detail questions ask you to find specific information that is explicitly stated
within the passage. Here are some examples of Detail question stems:
According to the author, which of the following is a type of rug found in
French castles?
The second step in constructing a picket fence is to
Which of the following is cited in the passage as an advantage of a
retirement account?
Notice how these questions are very different from Global questions. In
these types of questions, you do not have to read for the author’s main
idea. In fact, it is crucial in Detail questions not to overanalyze or read too
much into the question. The correct answer to these questions will almost
always be a paraphrase of something found directly in the passage.
Beware of the difference between simply recognizing text from the passage
and recognizing text from the passage that answers the question. Wrong
answer choices will sometimes be pulled from irrelevant areas of the given
text. For Detail questions, always research the text, make a prediction, and
then find a match for that prediction among the answer choices.
Below, take a look at how a Kaplan-trained test taker approaches a typical
Paragraph Comprehension Detail question. Remember to start with the
question stem, labeled with “Step 1” below.
Question
Analysis
Question
Analysis
The dancer and choreographer
Step 2: Read the passage,
Martha Graham is regarded as
one of the outstanding
innovators in the history of
looking for why Graham
introduced new techniques.
The passage starts with
dance. In a career that lasted
over 50 years, Graham created
more than 170 works ranging
background information
regarding Martha Graham and
her accomplishments. Then, her
from solos to large-scale pieces,
and danced in most of them
dancing background and training
are discussed. The final sentence
herself. Trained in a variety of
different international styles of
dance, she began in the early
discusses why she created a new
dance style.
1920s to break away from the
rigid traditions of classical ballet.
The passage starts with
background information
She wanted to create a new
dance form that would reflect the
transformed atmosphere of the
regarding Martha Graham and
her accomplishments. Then, her
dancing background and training
postwar period.
are discussed. The final sentence
discusses why she created a new
dance style.
Martha Graham’s motivation for
Step 1: This is a Detail question.
introducing new dance
techniques was to
You are looking for a reason why
Martha Graham introduced new
dance techniques.
Question
Analysis
Step 3: Rephrase the last
sentence of the passage: Graham
introduced new dance
techniques because she wanted
to come up with a new, original
dance form that expressed the
way the world felt a er the war.
(A) break away from the
Step 4: This choice describes
traditions of classical ballet
what Graham did, but is incorrect
because it does not answer the
given question of why she did it.
(B) attract attention to her dance
This is a distortion of what the
troupe
passage said. While attracting
attention may have been a nice
side effect, it’s not the reason
why Graham introduced new
dance techniques. Incorrect.
(C) express the changed mood of
her time
Correct. This matches the
prediction.
Question
(D) emphasize the rigidity of
conventional dance movement
Analysis
This is incorrect because it
distorts Graham’s intention. She
was not commenting on
conventional dance movement.
She was updating dance to
reflect the current times.
Now, you take a shot! Use the example above to help you through the
following practice item. Make sure to follow the Kaplan Method to secure
great habits for Test Day.
Golden retrievers, one of the most popular dog breeds
in the United States, have earned their wide
acceptance for a variety of reasons. As hunting dogs,
they will retrieve game carefully and willingly bring it
back to the hunter without damage. As family pets,
goldens are gentle and patient additions to the
household, willingly abiding unintentional abuse by
toddlers. Goldens are intelligent and can be readily
trained to respond to a wide variety of commands. For
this reason, they are among the favorite breeds chosen
to be trained as assistance dogs for disabled persons.
Also, their friendly nature has made them perfect
visitors to communities for the elderly. A golden
retriever will do its utmost to please its human master.
The author states that golden retrievers are excellent
assistance dogs because they are
(A) friendly
(B) intelligent
(C) gentle
(D) available
Explanation
Step 1: The question asks for what the passage states is the reason why
golden retrievers are excellent assistance dogs. This is a Detail question.
Step 2: The passage discusses various reasons for why golden retrievers
are so popular. Sentences four and five describe the attributes that make
golden retrievers excellent assistance dogs.
Step 3: Combine sentences four and five to formulate your prediction:
goldens are excellent assistance dogs because they are intelligent and easily
trained.
Step 4: Answer choice (B) matches the prediction that goldens make great
assistance dogs because they are smart and easily trained. Because the
other answer choices don’t match the prediction, we can eliminate them.
ASVAB STRATEGY
To correctly answer Detail questions:
Identify specific information in the passage that answers the
question.
Don’t fall for answer choices that rephrase statements in the
passage but that don’t answer the question.
INFERENCE QUESTIONS
Sometimes the ASVAB will ask you questions about the passage to which
the answers are not directly stated in the text but are instead implied by
the passage. Here are just a few of the ways an Inference question might be
worded:
Which of the following is implied by the passage?
The author apparently feels that
It can be inferred from the passage that
As you can see, the wording in Inference questions rarely points you to a
specific part of the passage, as Detail questions do. And Inference
questions won’t necessarily ask you about the ideas that are most
important to the author, as Global questions do. Instead, Inference
questions require you to consider multiple statements in a passage and,
from them, determine what else the author must believe. Because there
are many inferences that can be made from a given piece of text, it’s not
necessary to predict before considering the answer choices. Rather,
paraphrase the passage and move through the answer choices, selecting
the one that is supported by the given text.
Because the correct answer to an Inference question is simply the one
answer choice that is fully supported by what is stated in the passage, you
can also eliminate wrong answer choices because they commit one of the
following errors:
They contradict information in the passage.
They bring in outside information that is not discussed in the passage.
They distort the information presented in the passage.
They make an extreme claim that is not completely supported by the
passage.
Let’s see how a Kaplan-trained test taker handles a Paragraph
Comprehension Inference question. Remember to start with the question
stem, labeled with “Step 1” below.
Question
Analysis
Dan and Sonya are married and
have exactly three children–
Betty, George, and Tara–and
exactly three grandchildren.
George usually babysits Betty’s
Step 2: The passage starts with
background on Dan and Sonya,
who are married and have three
children: Betty, George, and Tara.
They also have three
twin daughters, while Tara
usually babysits George’s child.
grandchildren. The passage
states that Betty has twin
daughters, and that George has a
child.
Question
If these statements are true,
which of the following must be
true?
Analysis
Step 1: This question asks what
must be true based on what the
passage stated, so it’s an
Inference question. Because
there are no clues in the question
stem pointing to a single area of
the text, read and paraphrase the
entire passage.
Step 3: Mentally or on scratch
paper, create a “family tree” to
visualize the relationships:
This is a summary of the given
information. Since there are only
three grandchildren, this means
that Tara must not have any
children.
(A) All of Dan’s grandchildren are
female.
Step 4: Though Betty has two
daughters, the sex of George’s
child is not known. Therefore, it’s
not necessarily true that all of the
grandchildren are female.
Eliminate.
Question
(B) Tara has no children.
Analysis
Correct. This must be true
according to the statements in
the passage.
(C) Tara sometimes babysits for
Betty’s children.
Though the passage states that
Tara usually babysits George’s
child, it does not mention
whether she ever babysits for
Betty or not.
(D) Sonya has at least one
grandson.
From the statements given in the
passage, all that is known for
sure is that Sonya has two
granddaughters and another
grandchild, whose sex is
unknown.
Now, you try it. Follow the steps used in the example above to help you
master your technique for tackling Inference questions on Test Day.
In each of the last three years, a court in this country
has awarded a settlement in excess of $300 million.
This is a travesty of justice, and it unfairly burdens the
court system. To alleviate the strain on the nation’s
court system, _________________.
Which of the following best completes the above
passage?
(A) there should be fewer lawsuits
(B) lawsuits should name more than one defendant
(C) courts should cease awarding excessive
settlements
(D) settlements should be awarded based solely on
need
Explanation
Step 1: The question asks what would complete the passage. Since the
correct answer will be based on what was said in the rest of the passage,
this is an Inference question.
Step 2: The passage states that, in the past three years, courts have been
awarding extremely high settlements. The author feels that these awards
are outrageous, saying that they are a “travesty of justice” and they
“unfairly burden the court system.”
Step 3: The gist of the argument is that awards are too big, so it would
seem logical that if courts stopped going overboard in awarding
settlements, it would help lessen the burden on the courts.
Step 4: The correct answer here is choice (C), that courts should stop
awarding excessive settlements. Answer choices (A) and (B) are not issues
discussed in this passage. Choice (D), likewise, is not discussed in the
passage, and the use of “solely” makes it too extreme as well. There is
nothing in the passage to support that settlements should be awarded only
based on need.
ASVAB STRATEGY
To correctly answer Inference questions:
Remember that the correct answer is supported by statements in
the passage.
Don’t read between the lines too much.
Eliminate choices that introduce details or opinions the author
doesn’t mention.
Vocabulary-in-Context Questions
One final type of question found in the PC section will ask you for the
meaning of a word used in the paragraph. These questions, which we call
Vocabulary-in-Context questions, are pretty straightforward: the correct
answer will be a word that can replace the word in question without
altering the meaning of the sentence.
To handle this question type, focus on the word in the question stem while
you are reading the passage. Then, predict an answer by defining the word
as it is used in context. Finally, attack the answer choices by looking for a
word that matches your prediction. Once you have selected an answer
choice, reread the initial sentence with the answer choice in place of the
vocabulary word to be sure the meaning of the sentence is the same.
If you feel as though your vocabulary could use some improvement, be
sure to utilize the vocabulary-building resources available to you in
chapter 3 (Word Knowledge) and in the Appendix.
Below, take a look at how an expert uses the Kaplan Method to efficiently
and effectively attack a Vocabulary-in-Context passage. Remember to start
with the question stem, labeled with “Step 1” below.
Question
Analysis
When voters choose a candidate
Step 2: The word scheme is used
in an election, they cast one vote
for one candidate. However,
there are other ways that votes
can be cast in different situations.
One of the more common
in the fourth sentence of the
passage. Leading up to the word,
the passage is talking about the
process of choosing a candidate
in an election.
alternatives is rank voting. In this
scheme, each voter ranks the
choices from first to last. Thus, if
there were ten positions to fill,
each voter would assign ten
points to her favorite choice, nine
points to the second favorite, and
so on. This system is used by the
Associated Press to rank college
sports teams and a modified
version is used in Australian
elections.
Question
A word that could be properly
substituted for scheme in the
passage is
Analysis
Step 1: The question asks you to
determine the meaning of a word
used in the passage. This is a
Vocabulary-in-Context question.
Step 3: There are different
approaches to elections listed.
This tells us the word is being
used to describe a procedure or a
process. One of those words, or a
synonym, would be a good
prediction for the meaning of the
word scheme in this passage.
(A) plot
Step 4: While a common usage of
the word scheme is to describe a
plot, no one is plotting anything
in the passage.
(B) collection
Collection does not make sense in
the context of the passage.
Eliminate.
(C) vision
Vision does not make sense in the
context of the passage. Eliminate.
Question
(D) method
Analysis
Correct. This scheme refers to
rank voting, which is a method of
voting.
Now it’s your turn. Follow the steps used in the example above to correctly
and confidently answer the Vocabulary-in-Context question below.
Who was the first man to discover the North Pole?
Soon after the turn of the twentieth century, two men
each claimed the honor individually. While Frederick
Cook claimed he was the first to discover the North
Pole in 1908, Robert Peary disputed Cook’s account
and set out on his own expedition in 1909. Today, it is
unclear which man, if either, actually reached the
North Pole. After poring through the written accounts
of Cook and Peary’s expeditions, researchers believe
that while both men came close to the North Pole,
neither man actually found it.
As used in the passage, “poring through” most nearly
means
(A)
(B)
(C)
(D)
reading carefully
filtering out
searching for
making notes in
Explanation
Step 1: How is the phrase “poring through” being used in the passage in
this Vocabulary-in-Context question?
Step 2: The researchers had access to Cook and Peary’s written accounts,
so they must have evaluated them by reading through them.
Step 3: Anything that expresses the idea of “reading” the accounts will be
correct.
Step 4: Only answer choice (A), reading carefully, matches. Answer choice
(B), filtering out, changes the meaning of the sentence: the researchers
weren’t removing some of the written accounts. Similarly, the researchers
weren’t searching for the accounts, (C), since it’s inferred that they already
had the documents. Same with answer choice (D): the researchers were
not making notes in the explorers’ accounts.
ASVAB STRATEGY
To correctly answer Vocabulary-in-Context questions:
Many words and phrases have different meanings depending on
their context. Think about the term’s specific meaning in the
passage.
Always make a prediction before you look through the answer
choices.
The correct choice will not change the meaning of the sentence.
PARAGRAPH COMPREHENSION
PRACTICE SET 1
For each question, read the paragraph and select the answer that
best completes the statement or answers the question that
follows. This question set has 10 questions, which is the number
of Paragraph Comprehension questions you will see if you take
the CAT-ASVAB.
1. Four years ago, the governor came into office seeking to change
the way politics were run in this state. Now, it appears she has
been the victim of her own ambitious political philosophy. Trying
to do too much has given her a reputation as being pushy, and the
backlash in the state has let her accomplish little. She may very
well lose in her reelection bid.
The governor’s approach to politics was
(A) business as usual
(B) overly idealistic
(C) careless and sloppy
(D) influenced by his critics
2. Since its first official documentation by Sir George Everest in 1865,
Mount Everest in Nepal has been the “Holy Grail” of
mountaineers. Sir Edmund Hillary of New Zealand and Tenzing
Norgay of Nepal were the first men to successfully complete the
ascent to the peak in May 1953. This feat won them international
acclaim, not to mention knighthood for Hillary. But much less
celebrated is the first successful ascent of Everest by a woman,
which did not take place until May 16, 1975. Junko Tabei of Japan
was the first woman to reach the summit of the world’s most
famous single peak. The first American woman to scale its heights
successfully was Stacy Allison of Portland in 1988.
A member of the first successful Mount Everest expedition was
(A) Sir George Everest
(B) Junko Tabei
(C) Sir Edmund Hillary
(D) Stacy Allison
3. It is without question a travesty that our children are no longer
given healthy, nutritious food options for lunch in our public
schools. Hamburgers, pizza, and chocolate are not only giving our
kids bigger waistlines, but these junk foods are also helping teach
them poor eating habits. It is imperative that we change the
mindset that any food is good food and start offering students
better meals at the same prices. Otherwise, a new generation of
obese Americans is a given.
According to the passage, over the past few years, school lunches
have gotten
(A) more expensive
(B) more exotic
(C) healthier
(D) less nutritious
4. Many times families choose to replace old furniture when just a
minor amount of maintenance is all that is needed. To fix a
wooden chair that is wobbly, follow these easy steps. First, check
the joints of the chair to see if the chair is structurally sound.
There should be small dowel rods and a corner block to keep the
chair together. Next, use a ripping chisel to remove the corner
block. Once the block is free from the chair, you should be able to
glue the joints back together. Finally, once the glue looks dry,
place the corner block back on the chair and gently mallet the
block onto the dowels. In no time, you will have saved not only
the chair, but also your hard-earned money!
A er removing the corner block, you should
(A) mallet the dowels into place
(B) check the joints for damage
(C) glue the joints together
(D) replace the corner block
5. James felt the pulse of the crowd. There was a low murmur just
under the house music. Backstage, his bandmates were tuning or
drumming lightly on tabletops. In a few moments, the whole
country would watch the band play. What a change from those
dingy bars and clubs a few years ago. Maybe all the hard work had
finally paid off. Looking down at his callused hands, he wondered
if maybe this would be the break they had been working so hard
for.
The tone of this passage is one of
(A) sadness
(B) anticipation
(C) anger
(D) ambivalence
6. Packaging on many popular foods is deceiving to consumers. Too
o en, the print is small and hard to read. And if you can read it, it’s
o en confusing or intentionally vague. This is especially true on
the nutrition label. The government really ought to do something
about the nutrition labels on food because the existing laws just
don’t go far enough.
The author would probably support which of the following?
(A) magazine advertisements for cigarettes
(B) allergy information prominently listed on food labels
(C) fine print on a contract
(D) food ads in the Sunday paper
7. In an age where we have pills for depression, dysfunction, and
aggression, not to mention headaches, it is important that we not
forget that many drugs can have serious side effects. These may
range from internal bleeding, vomiting, or soreness in the limbs
to, in more extreme cases, loss of consciousness or even coma. If
you experience unwanted side effects, it is important to get to a
hospital immediately and seek treatment. Drinking alcohol or
smoking cigarettes may also contribute to violent side effects.
According to the passage, one of the possible side effects of drugs
is
(A) drinking alcohol
(B) dysfunction
(C) internal bleeding
(D) aggression
8. First created at the height of atomic postwar paranoia, the
Incredible Hulk stories offer a fascinating look at the dual nature
of human beings. On the one hand, he is a mild-mannered,
bespectacled scientist. On the other, he is a raging, rampaging
beast. More than a statement about nuclear dangers, the Hulk is a
reflection of the two sides in each of us—the calm, logical human
and the raging animal.
According to the author, the comic book character of the Hulk is
(A) a reflection of humanity
(B) really an animal
(C) mild mannered
(D) a protest about atomic power
9. Once considered the best high school player in the country, the
onetime prodigy now spends his days working as a bricklayer for
a local construction company. Asked if he is bitter about the way
his life turned out, he replies, “Not at all.” In fact, he says, his only
regret is that he didn’t study hard enough and go to college. He
still gets recognized on occasion, but an extra 80 pounds and bad
knees keep him from reliving his former glory on the court.
The word prodigy in the passage most nearly means
(A) depressed loner
(B) shy scientist
(C) gi ed youngster
(D) bitter malcontent
10. Celebrated as one of the greatest film directors of the twentieth
century, Alfred Hitchcock made his name creating some of the
most critically acclaimed suspense films of all time. But while
other directors of the genre seemed content telling stories of
domestic intrigue, Hitchcock was not afraid to make films
centering on unconventional subjects. In fact, one of his most
celebrated films, The Birds, has no typical antagonist: the
suspense comes not from a person who is out to do wrong, but
rather from nature itself.
The main idea of the passage above is that
(A) Alfred Hitchcock is one of the greatest film directors ever
(B) most suspense films tell stories of domestic intrigue
(C) Alfred Hitchcock was not afraid to tell unconventional stories
(D) The Birds is scarier than traditional suspense films
PARAGRAPH COMPREHENSION
PRACTICE SET 2
For each question, read the paragraph and select the answer that
best completes the statement or answers the question that
follows. This question set has 10 questions, which is the number
of Paragraph Comprehension questions you will see if you take
the CAT-ASVAB.
11. Bassoons are double-reeded wood instruments that produce a
deep baritone sound. A bassoon’s pitch can be altered by
adjusting a curved tube called a bocal. The deeper the bocal is
inserted into the bassoon, the higher the pitch. Conversely,
pulling the bocal out of the instrument lowers the pitch.
It can be inferred from the passage that the bassoon
(A) is a larger instrument than the oboe
(B) is the deepest-sounding wood instrument
(C) is the only instrument that utilizes a bocal
(D) is capable of a range of pitches
12. Investors who believe that a company’s stock price is overvalued
can perform an action called a “short sale.” To short a stock, an
investor sells shares that she does not currently own; typically,
shares for short selling are borrowed from a broker. If the stock
goes down in price, the investor is able to buy the shares at a
lower price. Shorting stocks is risky, though; if the stock suddenly
rises in price, the broker can force the investor to purchase the
shares at the higher price, resulting in a significant loss.
According to the passage, an investor who shorts stocks first
(A) buys shares of a company’s stock, then sells those shares for
a loss
(B) sells shares of a company’s stock, then buys those shares at a
later date
(C) buys shares of a company’s stock, then sells those shares
whenever he wishes
(D) sells shares of a company’s stock, then uses that money to
buy stock in another company
13. As rays of sunlight peeked through the tops of the trees, Mark felt
at peace. It had been years since he had walked these trails.
Everything was quiet and calm. It seemed to him that he finally
saw the woods as they truly were: a refuge, a place to be renewed,
a respite from the clamor and chaos of the city.
In this passage, respite most nearly means
(A) relief
(B) opposite
(C) valley
(D) hope
14. The bus system in the city is in need of a drastic overhaul. Last
week, the Main Street bus line was reduced from one bus every 15
minutes to one bus an hour. The week before that, the Uptown
bus was canceled completely. Each change occurred with no
notice! If the city expects people to continue to use public
transportation, it needs to reduce the bus system issues.
Which of the following is mentioned in the passage?
(A) The city needs to notify customers of bus line interruptions.
(B) The city should allocate money from other programs to
revamp the bus system.
(C) The Main Street bus line has experienced reduced service in
the past.
(D) The Main Street bus line has been shut down in the past.
15. The European hedgehog is found in a wide range of habitats in
Western Europe. It is quite popular because of its charming
appearance and because of its appetite for many of the pests that
plague European gardens. Unlike warmer-climate species of
hedgehog, the European hedgehog is known to hibernate in the
winter. It is a solitary animal, although occasionally a male and
female will share a hibernation nest. While currently stable across
much of continental Europe, the population of European
hedgehogs is thought to be declining severely in Great Britain.
Which of the following best describes the topic of this passage?
(A) the decline of the European hedgehog in Great Britain
(B) why the European hedgehog is popular among European
gardeners
(C) the characteristics and behavior of one species of hedgehog
in Europe
(D) the hibernation habits of European hedgehogs
16. Questions 7 and 8 refer to the following paragraph.
In 1918, as the world prepared to celebrate the end of World War I,
a stealthier form of death appeared: the so-called “Spanish
influenza.” It is said that this strain of influenza killed more in a
single year than the bubonic plague killed in a century. The
outbreak gave modern scientists their first close look at a
worldwide pandemic and paved the way for great advances in
medicine. Furthermore, the unprecedented number of patients
led to a boom in the medical field. One lasting result was an
increase in pay for doctors, encouraging many to enter the
profession. It could be said that the Spanish flu introduced the
idea of “medicine for profit” to the world.
It can be inferred from the passage that
(A) advances in medicine in the early twentieth century would
not have happened without the outbreak of the Spanish flu
(B) scientists know little about the cause of the bubonic plague
(C) a doctor today might not have chosen to enter the medical
profession before World War I
(D) the huge numbers of Spanish flu patients overwhelmed the
available medical care and resulted in dra ing more doctors
to deal with the epidemic
17. In the context of the paragraph, the word unprecedented most
nearly means
(A) extraordinary
(B) tragic
(C) perplexing
(D) advantageous
18. Before the Great Chicago Fire of 1871 was extinguished, rumors
circulated that it had been caused by the now infamous “Mrs.
O’Leary’s cow.” Yet, a er nine days of questioning fi y people,
investigating authorities issued an inconclusive report about the
fire’s cause. “Whether it originated from a spark blown from a
chimney on that windy night,” the report read, “or was set on fire
by human agency, we are unable to determine.” Besides Catherine
O’Leary and her cow, suspects at the time included several
colorful residents of Chicago’s immigrant community, including
“Peg Leg” Sullivan, who had first alerted the O’Leary family to the
fire. In the end, it is likely that the true cause or culprit will never
be known.
Which of the following statements best expresses the main idea of
the passage?
(A) Although the investigation was inconclusive, it is now
considered likely that Catherine O’Leary’s cow was the true
cause of the Chicago fire.
(B) Investigative authorities believed that the Chicago fire was
set by an unknown suspect rather than being an accidental
event.
(C) Investigators considered “Peg Leg” Sullivan to be a more
likely suspect than Catherine O’Leary in causing the Chicago
fire.
(D) The cause of the 1871 Chicago fire will probably never be
determined.
19. Despite his famous theories about how children are sexual beings
who may develop into adults with unconscious psychological
conflicts, Freud had only one patient during his lifetime who was
actually a child. But this fact alone is not sufficient reason to
dismiss his entire theory. Many of his ideas were based on
information gained from reliable case histories of his adult
patients. While some of his conclusions have been questioned in
light of recent findings in neuropsychology, his most noteworthy
contributions to psychology stand up against the criticisms of
those who accuse him of fabricating his evidence to confirm his
preconceived theories.
The author would most likely agree with which of the following?
(A) Neuropsychology has recently proven that Freud used
unreliable evidence to support his theories.
(B) Although recent science has weakened some of Freud’s
theories, he should still be seen as having made significant
contributions to psychology.
(C) Freud’s most famous theories are called into question by the
fact that he based them all on one child patient.
(D) Freud’s theories of child sexuality have been confirmed by
numerous case histories.
20. At the beginning of the universe, temperatures were incredibly
high. During this period of high energy, vast amounts of hydrogen,
helium, and lithium were created. Although hydrogen and helium
are still abundant, scientists believe that the amount of lithium
currently measured comprises only about a third of what we
should expect to see. There are a wide variety of explanations for
why this might be, including some involving hypothetical
elementary particles known as axions. Others believe that lithium
is trapped in the core of stars, making it undetectable by our
current instruments. Of the many theories proposed, there is no
clear front-runner to explain the absence of lithium in the
universe.
According to the passage, axions have been hypothesized in order
to
(A) show how lithium was created at the beginning of the
universe
(B) explain why scientists detect less lithium in the universe than
expected
(C) explain why hydrogen and helium make up most of the mass
of the universe
(D) support the belief that lithium has become trapped in the
core of stars
Answers and Explanations
PARAGRAPH COMPREHENSION PRACTICE SET 1
1. B
From the information given, you should have seen that the governor
was very determined to get things done her way. So her approach
could hardly be described as business as usual, choice (A). Nowhere in
the passage is her approach described as careless and sloppy, choice
(C). And since the mayor insisted on doing things her way, her
approach was not influenced by her critics, choice (D). Only (B) is
addressed in the paragraph. Seeking to change the way politics are run
indicates an idealistic approach to politics.
2. C
This Detail question asks you for a member of the first expedition to
conquer Mount Everest. Researching the passage, you must be careful
not to assume that the mountain is named for its conqueror. While Sir
George Everest, (A), first documented and recorded the height of
Everest in 1865, it was (C) Sir Edmund Hillary who, along with Tenzing
Norgay, completed the first ascent to the peak in 1953. The question
does not ask for the first woman, or the first American woman, to reach
the summit, so (B) Junko Tabei and (D) Stacy Allison are out. The
correct answer is (C).
3. D
The author feels strongly that meals in school cafeterias have become
more and more similar to junk food. Choice (A) is not applicable,
regardless of its validity, because it is not the central point of the
passage. Choice (B) is nowhere indicated in the passage, and choice (C)
is the opposite of the correct answer. Of the answer choices given, only
choice (D), less nutritious, correctly answers the question.
4. C
This Detail question asks you to identify a specific step in a process, so
your first task is to locate the step that discusses removing the corner
block. Removing the corner block is mentioned in the fi h sentence.
A er using a ripping chisel to remove the block from the chair, the
worker is free to glue the joints back together to tighten them, choice
(C).
5. B
To correctly gauge the tone of a passage, you should pay attention not
only to the details, but also to the language and description. In this
passage, James is clearly waiting to go onstage. Words like pulse,
murmur, and maybe invite the reader to feel excitement and
nervousness as James does. Of the answer choices given, (D),
ambivalence, is clearly wrong, as James definitely cares about what is
going to happen. He seems wistful, but never sad, (A), or angry, (C).
The only answer that successfully captures James’s mood is choice (B),
anticipation.
6. B
Judging from the critical tone of the author and the subject matter at
hand, one can safely assume that the author is interested in public
safety. Clearly small print is not going to be favored by this author, so
choice (C) is out. Choice (D) doesn’t make sense and choice (A) is not
something thought of as good for public safety. Choice (B), allergy
information prominently listed on food labels, fits the author’s passion
for consumer labels.
7. C
According to the details of the passage, one possible side effect from
prescription drug usage is internal bleeding, answer choice (C).
Drinking alcohol, (A), can exacerbate side effects, but it is not a side
effect itself. Dysfunction, (B), and aggression, (D), are discussed as
conditions treated by drugs, not as side effects of drug use.
8. A
From the details of the passage, it is clear that the author sees the
character of the Hulk as a symbol. The passage states that the Hulk is a
reflection of the two sides of each of us, which matches choice (A) a
reflection of humanity. The passage states that the Hulk varies between
an animal mentality, (B), and a mild-mannered person, (C), but it does
not claim that he is one over the other. While the passage mentions
“atomic postwar paranoia,” it does not suggest that the Hulk is used as
a protest of any type, as in choice (D).
9. C
According to the passage, the onetime star athlete is now a local
bricklayer. There is nothing in the passage to indicate that the person
in question was ever a depressed loner (A), shy scientist (B), or bitter
malcontent (D), but it only makes sense that he was once a gi ed
youngster (C). The term “prodigy” refers to a person with natural
ability, o en at a young age.
10. C
Remember to look to contrast keywords to help determine an author’s
main point. Here, the passage makes a distinction between the work of
typical directors and that of Hitchcock: Hitchcock, unlike the others,
dared to make films that were unconventional, which is answer choice
(C). While answer choices (A) and (B) are supported by the passage,
they are too narrow to encompass the main point. Answer choice (D) is
out of scope and is not stated or implied in the passage.
PARAGRAPH COMPREHENSION PRACTICE SET 2
11. D
While it may be true that the bassoon is larger than the oboe, that
claim is not supported by information in the passage, so (A) is out. The
passage does state that the bassoon produces a deep sound, but
claiming that it is the deepest-sounding wood instrument is too
extreme, so (B) is out. Nothing in the passage supports the claim that
the bassoon is the only instrument that utilizes a bocal, which means
(C) is incorrect. The passage does state that a bassoon’s pitch can be
altered by adjusting the bocal, so (D) is correct.
12. B
In this Detail question that asks about a process, refer back to the
passage to find the correct answer. You will find the information in the
second, third, and fourth sentences. The second sentence states that
an investor sells shares she does not currently own, while the third and
fourth sentences indicate that she then purchases those shares at a
later date. That sequence is described in answer choice (B). Both (A)
and (C) are incorrect because a short seller does not first buy shares of
stock. (D) is out because although a short seller does first sell shares of
stock, nothing in the passage indicates that that money is then used to
purchase stock in another company.
13. A
Always make a prediction in Vocabulary-in-Context questions. The
tone of this passage is one of peacefulness and calm. Therefore, you
could infer that Mark’s quiet, relaxing walk in the woods is a break, or a
period of relief, from the clamor and chaos of the city. While (B)
opposite might sound appealing, since the passage contrasts the forest
with the city, opposite doesn’t make sense if inserted into the
sentence. Mark might be in a (C) valley, but that also doesn’t make
sense if inserted into the sentence. Finally, (D) hope doesn’t match the
idea that Mark has simply found a quiet place away from the city.
14. C
This statement is a specific detail taken from the second sentence of
the passage, “the Main Street bus line was reduced from one bus every
15 minutes to one bus an hour.” There is no evidence that the Main
Street bus line has ever been completely shut down, (D). The author
does mention not being given any notification, but he does not state
choice (A), that the city needs to notify customers. Choice (B) might be
an idea the author would agree with, but it is not mentioned in the
passage.
15. C
The author introduces the European hedgehog as “a species” of
hedgehog in the first sentence, comparing it to other species. The
passage then provides information about the European hedgehog’s
eating and hibernation habits, as well as the males’ aggressive
behavior. Choice (C) captures the paragraph’s focus and is the correct
answer to this Global question. Choices (A), (B), and (D) all mention
facts given in the passage but miss the big picture by narrowly
focusing on only one idea.
16. C
The question asks for an inference that can be drawn from the passage
but provides no clues about the nature of the inference. Each answer
choice must be compared with the information given to identify the
one choice that must be true based on the passage. The correct
answer is supported by the fi h sentence, “One lasting result was an
increase in pay for doctors, encouraging many to enter the profession.”
If many people were encouraged to become doctors because of higher
pay, we can infer that lower pay before World War I was a deterrent to
entering the profession. The word “lasting” implies that higher pay is
still motivating more people to become doctors today. Choice (A) is
extreme; even though the flu brought about advances, you cannot
infer that advances would not have happened anyway. Choice (B) is
unsupported by any facts presented. Choice (D) distorts the facts
given. Doctors were encouraged by higher pay, not dra ed. Also, there
is no evidence that medical care was overwhelmed by the
unprecedented numbers of patients. In fact, the patients caused a
“boom” in the field.
17. A
This Vocabulary-in-Context question asks about the author’s use of the
word unprecedented. The author uses the word to describe the
increase in the number of patients, which had a lasting impact on the
medical profession. To have such a significant effect, the number of
patients must have been unusual, or extraordinary. Choice (B), tragic,
might be tempting because of the number of people who died. But this
meaning does not fit the point of the sentence. Choice (C) can be
eliminated because the text does not suggest that the number of
patients was perplexing, or puzzling. Choice (D), advantageous, would
suggest that the author thinks the number of patients was beneficial,
which is not the author’s point at all. The change in the medical
profession may or may not have been advantageous; the author gives
no opinion.
18. D
This Global question asks for the author’s main idea. The word “Yet” in
the second sentence signals the author’s key point: authorities were
unable to establish the cause of the fire. The final sentence reinforces
this point. The rest of the text discusses the investigation of the fire
and speculation about its causes. Thus, choice (D) is correct. Choice (A)
is never stated or implied in the passage. Choice (B) contradicts the
quote from the report, which states that whether the cause was
accidental or intentional is unknown. Choice (C) is a distortion; “Peg
Leg” Sullivan was considered as a suspect, but no likelihood of his guilt
is proposed.
19. B
The correct answer to this Inference question will reflect an opinion
given by the author in the text. The first sentence points out a
perceived problem with the data supporting one of Freud’s theories.
The author then states an opinion in the second sentence that this
weakness in the data is not enough to dismiss Freud’s ideas. The rest
of the paragraph supports this claim, ending with the opinion that
Freud’s contributions to the field of psychology still stand up. Choice
(B) sums up the author’s opinion. Choice (A) brings up an idea
presented, but the contrast word “While” in the passage indicates that
this is not the author’s opinion. Choice (C) brings up the problem with
Freud’s evidence mentioned in the first sentence. This, however, is the
point that the author dismisses in the second sentence. Choice (D)
distorts the author’s defense of Freud; the word “confirmed” is
extreme and does not match the author’s concession that some of
Freud’s conclusions have been questioned.
20. B
This Detail question asks about something specifically mentioned in
the passage. Axions are mentioned in the fourth sentence, which
begins “There are a wide variety of explanations for why this might be .
. . ” to introduce one proposed explanation for the unexpected scarcity
of lithium in the universe. Choices (A) and (C) both refer to the creation
of various elements, and the author does not mention axions in
relation to how the elements came into being. Choice (D) distorts the
idea of axions by joining it with another explanation, set apart in the
next sentence by the words “Others believe.”
REVIEW AND REFLECT
So, how did you do? What was challenging about these problems? Did
you notice that you were performing better on some question types than
others?
Going back over these problems may be helpful. As you review your
performance, ask yourself a few questions:
Were you able to identify different Paragraph Comprehension question
types?
Do you have a strategy for each of the different question types?
Are you reading Paragraph Comprehension passages strategically?
Can you separate background information, supporting details, and
main points?
Do you make accurate predictions?
Are you able to match your prediction to the correct answer?
Can you identify and eliminate common wrong answer types?
In future Paragraph Comprehension questions, apply what you’ve
learned in this chapter. Approach each question with Kaplan’s 4-step
method, and you’ll see your performance in this section continue to
improve.
Want more instruction and practice with Paragraph Comprehension? Log
in at kaptest.com/login to watch the video in this book's online
resources and try more questions in the Qbank.
CHAPTER 5
MATH STRATEGIES FOR THE ASVAB
Know What to Expect
O en the most efficient way to get the correct answer to a math problem is
to use a strategy rather than just to “do the math.” That’s especially true on
the ASVAB, since you cannot use a calculator on the exam. On some math
tests, if you get the wrong answer but show that you set up at least some of
the math correctly, you’ll still get partial credit. On the ASVAB, you only get
credit for a right answer. One advantage of this is that you will get credit for
the correct answer regardless of how you get to it.
The two math sections on the ASVAB are called “Arithmetic Reasoning” and
“Mathematics Knowledge.” Together they form the quantitative half of the
Armed Forces Qualifying Test (AFQT), so you’ll want to do well on these
sections no matter what your ultimate vocational aim in the military.
The Arithmetic Reasoning (AR) section tests your ability to handle
arithmetic word problems. The CAT version of this section gives you 55
minutes to answer 15 questions, while the paper-and-pencil version gives
you 36 minutes for 30 questions. This section is designed to measure your
ability to apply reasoning to solve problems involving common math
concepts. Many of the questions will be in the format of word problems.
Typical AR topics involve number properties, rates, percentages, ratios,
proportions, averages, and unit conversions.
The Mathematics Knowledge (MK) section tests your understanding of a
wide range of concepts in applied arithmetic, algebra, and geometry. The
CAT version gives you 23 minutes to answer 15 questions; the paper-andpencil version gives you 24 minutes to answer 25 questions. This section is
designed to measure general mathematical knowledge. You may see the
occasional word problem on the MK section of the ASVAB, but in general
the questions are more direct than the word problems found on the AR
section. For this reason, you are given less time per question on this
section than on the AR section.
The Kaplan Method for ASVAB Math
Questions
Learning Objectives
In this section, you will learn to:
identify your task on math problems
determine the most efficient strategy for getting the correct
answer
apply the Kaplan Method for ASVAB Math Questions
Working quickly and efficiently is essential to maximizing your score on
these sections. To accomplish this, use the Kaplan Method for ASVAB Math
Questions.
THE KAPLAN METHOD FOR ASVAB MATH
QUESTIONS
Step 1: Analyze the information given.
Step 2: Identify what you are being asked for.
Step 3: Solve strategically.
Step 4: Confirm your answer.
Step 1: Analyze the information given.
Read the entire question carefully before you start solving the problem. If
you don’t read the question carefully, you may make a careless mistake or
overlook the simplest approach to answering the question.
Step 2: Identify what you are being asked for.
Before you choose your approach, make sure you know what you’re
solving for. In other words, what does the correct answer choice represent?
This is an important step to keep you from falling for tempting wrong
answer choices. For example, if you are given an equation with two
variables, x and y, identify whether you are solving for x, for y, or for
something else. This step is important because the ASVAB may give you
wrong answer choices that represent the “right answer to the wrong
question.” That is, if you are asked to solve for x, one wrong answer choice
might represent the value of y.
Step 3: Solve strategically.
Once you understand what the question is asking for, it’s time to look for
the most strategic approach. Use your analysis from Steps 1 and 2 to find
the most efficient route to the correct answer. This step might involve
performing calculations (that is, “doing the math”), or it might be the case
that applying a strategy would get you to the correct answer more quickly.
This chapter will discuss these strategic approaches.
Step 4: Confirm your answer.
Reread the question a er you select your answer. Make sure you’ve
answered the question asked. If you notice that you missed something
earlier, rework the problem and change your answer if necessary.
Here’s an example of the Kaplan Method for ASVAB Math in action.
Question
Analysis
One bag contains 6 pieces of
candy, another bag contains 8
Step 1: The question tells you the
number of pieces of candy in
pieces, and a third bag contains
16 pieces. What is the average
three bags.
number of pieces of candy in a
single bag?
Step 2: Your task is to calculate
the average number of candies in
one bag.
Question
(A) 6
Analysis
Step 3: Use the average formula:
(B) 8
(C) 10
(D) 30
The average is 10, answer choice
(C).
Step 4: Don’t rework the math
from scratch; rather, ask yourself
whether the answer makes sense
given what you were asked for.
Does 10 seem like a likely average
given the numbers 6, 8, and 16?
Yes: Since the average of a set of
numbers has a value that’s
between the smallest and largest
numbers in the set, 10 makes
sense as an answer.
Strategies for Solving Math Problems
ASVAB Math Strategies
Backsolving
Picking Numbers
Strategic Guessing Using Logic
Combination of approaches
Several methods are extremely useful when you don’t know—or don’t have time to use—the
textbook approach to solving the question. In addition, performing all the calculations called for in
the question can o en be more time-consuming than using a strategic approach and can increase
the potential for mistakes.
Two problem-solving strategies that may be new to you are Backsolving and Picking Numbers.
These strategies are a great way to make confusing problems more concrete. If you know how to
apply these strategies, you’ll nail the correct answer every time you use them.
Strategic Guessing Using Logic and using a combination of approaches are other useful
shortcuts to getting more correct answers more quickly. Remember, you get points for correct
answers, not for how you got those answers, so efficiency is key to maximizing your score. This
section will discuss each of these strategies in turn.
BACKSOLVING
Sometimes it’s easiest to work backward from the answer choices. Since many Arithmetic
Reasoning questions are word problems with numbers in the answer choices, you can o en use
this to your advantage by using Backsolving. A er all, the test gives you the correct answer—it’s
just mixed in with the wrong answer choices. If you try an answer choice in the question and it fits
with the information given, then you’ve got the right answer.
Here’s how it works. When the answer choices are numbers, you can expect them to be arranged
from small to large (or occasionally from large to small). Start by trying either choice (B) or (C). If
that number works when you plug it into the problem, you’ve found the correct answer. If it
doesn’t work, you can usually figure out whether to try a larger or smaller answer choice next.
Even better, if you deduce that you need a smaller (or larger) number, and only one such smaller
(or larger) number appears among the answer choices, that choice must be correct. You do not
have to try that answer choice: simply select it and move on to the next question.
By backsolving strategically this way, you won’t have to try out more than two answer choices
before you zero in on the correct answer. To see an example of Backsolving, check out the
following problem and explanation.
Question
Analysis
An appliance store reduced the price of a
refrigerator by 20% and then raised the price
Step 1: The price of a refrigerator is reduced
20% and then that reduced price is raised
by 10% from the lower price. What was the
original price of the refrigerator, if the final
price was $70.40? Answer choices:
10%. The final price is $70.40.
Step 2: The correct answer represents the
original price, before the changes.
Question
Analysis
(A) $50
Step 3: To answer this question using algebra
(B) $70
(C) $80
would be complex and time-consuming and
would afford many opportunities for errors.
(D) $100
Instead, since all the answer choices are
numbers, backsolve.
Start by trying out (B) $70.
$70 reduced by 20%:
$70 − $14 = $56
$56 raised by 10%;
$56 + $5.60 = $61.60.
That’s lower than the final price of $70.40, so
choice (B) is too low. Eliminate both answer
choices (B) and (A).
Now try either (C) or (D). (D) is easier for a
percent problem.
Reduce $100 by 20%:
$100 − $20 = $80
Raise that $80 by 10%:
$80 + $8 = $88.
That final price is far too high, so (C) must be
the correct answer.
Question
Analysis
Step 4: The answer of $80 is the only one that
is neither too large nor too small to yield the
final price of $70.40 specified in the question.
Done.
In Backsolving, when you start with (B) or (C) and that answer doesn’t work, you’ll usually know
which direction to go. For example, if the answer choices are listed smallest to largest and (B) is too
large when you plug it in, you will know that (A) is the correct answer. If, on the other hand, (B) had
been too small, you would know that the answer was (C) or (D).
Now, try this one on your own. Use Backsolving.
(Hint: The hypotenuse (or longest side) of a right triangle is equal to the square root of the sum of
the squares of the other two sides. In other words, if the other two sides are a and b and the
hypotenuse is c, then a2 + b2 = c2.)
In the figure above, the circle with center O has a radius of 6 (in other
words, AO = 6). If AB = 10 and ∠OAB is a right angle, what is the length
of BC?
(A)
(B) 4
(C)
(D) 6
Explanation
Step 1: You are told that the length of the circle’s radius is 6, and you are given the length of one
leg of a right triangle that is partly embedded in the circle. Because the other leg of the triangle,
OA, is a radius of the circle, you know it has a length of 6. Also, a portion of the hypotenuse of the
triangle, OC, is another a radius of the circle and, likewise, has a length of 6.
Step 2: Your task is to determine the part of the hypotenuse outside the circle, or the entire
hypotenuse minus 6.
Step 3: You could use the Pythagorean theorem here: a2 + b2 = c2, where a and b are the lengths of
the legs of a right triangle and c is the length of the hypotenuse. However, a look at the answer
choices reveals that you might have to do some really burdensome calculations.
Instead, backsolve. Choosing between answer choices (B) or (C), start with (B) because 4 is much
easier to work with than
. If BC = 4, the hypotenuse would equal 4 + 6 = 10. Since
one of the legs has that same length, and the hypotenuse is always the longest side of a right
triangle, this is too short. Eliminate (A) and (B).
Next, try (D) 6. If BC = 6, the hypotenuse would equal 6 + 6 = 12. Using the Pythagorean theorem,
test to see if 62 + 102 equals 122. In fact, 36 + 100 does not equal 144, so the correct answer must be
(C).
Step 4: Because the other answer choices cannot be correct, choice (C) must represent the length
of BC.
PICKING NUMBERS
Another strategy that comes in handy on many Mathematics Knowledge questions and also on
some Arithmetic Reasoning questions is Picking Numbers. Just because the question contains
numbers in the answer choices, that doesn’t mean that you can always backsolve. There may be
numbers in the answer choices, but sometimes you won’t have enough information in the
question to easily match up an answer choice to a specific value in the question stem. For example,
a problem might present an equation with many variables, or it might give you information about
percentages of some unknown quantity and ask you for another percent. If the test maker hasn’t
provided you with a quantity that would be really helpful to have in order to solve the problem,
you may be able to simply pick a value to assign to that unknown. The other case in which you can
pick numbers is when there are variables in the answer choices.
When you are picking numbers, be sure that the numbers you select are permissible (follow the
rules of the problem) and manageable (easy to work with). In general, it’s a good idea to avoid
picking −1, 0, or 1 because they have unique number properties that can skew your results.
Here’s a great example showing how Picking Numbers can make an abstract problem concrete.
Question
Analysis
When n is divided by 14, the remainder is 9.
Step 1: An unknown number, n, is 9 larger
What is the remainder when n is divided by
than a multiple of 14.
7?
Step 2: The correct answer represents the
remainder when n is divided by 7.
(A) 1
Step 3: To make this abstract question
(B) 2
concrete, pick a number for n that leaves a
(C) 3
remainder of 9 when divided by 14. The most
(D) 4
manageable number to pick that is also
permissible in the problem is n = 23 (because
14 + 9 = 23). Now try out your number: 23 ÷ 7
= 3 with a remainder of 2.
(B) is the correct answer.
Step 4: Briefly look back over the math to
check that you are solving for the correct
value. Done.
Now, try this one on your own using the Picking Numbers strategy.
If a bicyclist in motion increases his speed by 30 percent and then
increases this speed by 10 percent, what percent of the original speed is
the total increase in speed?
(A) 10%
(B) 40%
(C) 43%
(D) 140%
Explanation
Step 1: The question gives information about two increases to the speed of a bicyclist.
Step 2: The question asks for the total percent increase.
Step 3: You are not told how fast the bicyclist is going when he starts his trip, so this is a great
opportunity for Picking Numbers. The easiest number to use in percent problems is 100, so start
the bicyclist at a speed of 100 miles per hour. Remember, the numbers you pick should be
permissible and manageable, but they do not have to be realistic.
The first increase in speed is 30%. Because 30% of 100 is 30, the new speed is 100 + 30 = 130. The
second increase in speed is 10%, but not 10% of the original speed—10% of the new speed.
Because 10% of 130 is 13, the final speed is 130 + 13 = 143. Subtract the original speed from the
final speed, and the increase in speed is 143 − 100 = 43. Since 100 was the initial number, 43 is
simply 43% of the original, answer choice (C).
Step 4: When confirming the answer for questions that ask about multiple percent changes, make
sure that you calculated the percent changes appropriately and didn’t simply add the percentages
given in the question, as (B) does. Also, check to make sure that you solved for the correct value,
here the increase in speed as a percentage of the original speed. Answer choice (D) makes the same
mistake as (B) but may look tempting to some test takers, because it is close to the final speed of
143.
When there are variables in the problem and in the answer choices, you can pick numbers for
those variables. Evaluate the expression in the question stem using your chosen numbers and then
evaluate each answer choice using the same numbers. Your goal is to find the answer that yields
the same numerical result as the one you calculated using your chosen numbers. When you use
this method, you must evaluate all of the answer choices. If more than one yields the same
numerical result, choose a different set of numbers to evaluate only the remaining choices that
gave matching solutions with the first set of numbers that you chose.
To solve problems containing variables in the question stem and answer choices using Picking
Numbers, start by picking permissible and manageable numbers for the variables. Answer the
question using the numbers you’ve picked. This answer is your target number. Then, substitute the
numbers you picked for the variables into the answer choices. You are looking for the answer
choice that gives you the target number.
Take a look at this example.
Question
Analysis
Question
Analysis
Camilla spent d dollars on groceries each
Step 1: The question contains no numbers;
week for w weeks, and p percent of the
amount she spent on groceries was spent on
only variables:
d = the amount Camilla spent on groceries
fresh vegetables. How much money did she
spend over the whole time period on
groceries other than fresh vegetables?
each week
w = the number of weeks she shopped
p = the percent of that money that went to
fresh vegetables.
Step 2: The correct answer represents the
amount of grocery money not spent on fresh
vegetables.
(A)
(B)
(C)
(D)
Step 3: Make this problem concrete by
replacing all the variables with numbers. Pick
manageable numbers:
d = 20
w=5
p = 10
With those numbers, Camilla spent $20 a
week on groceries for 5 weeks, for a total of
$100. 10% of that, or $10, was on fresh
veggies. This means that $100 − $10 = $90
was on other groceries. $90 is the target
number.
See what number results from plugging the
same values into choice (A):
Question
Analysis
That matches! However, because you chose
numbers for the variables, more than one
answer might match the target number. Keep
testing the other answer choices.
(B)
Incorrect.
(C)
This will be negative, which is incorrect.
(D)
Incorrect.
Only one answer choice, (A), matches the
target number, so it is correct.
Step 4: Briefly look back over the math you
did when checking choice (A). If you plugged
in the numbers correctly, you’re done.
Try this one on your own. Use the Picking Numbers strategy.
For all r, s, t, and u, what does r(t + u) − s(t + u) equal?
(A) (r + s)(t + u)
(B) (r − s)(t − u)
(C) (r + s)(t − u)
(D) (r − s)(t + u)
Explanation
Step 1: You are given an algebraic expression and asked to find an equivalent expression.
Step 2: The correct answer simplifies the expression r(t + u) − s(t + u).
Step 3: Since you are given no values for any of the four variables, you can pick numbers for each
of them. Some good numbers to pick here are r = 5, s = 4, t = 3, and u = 2. You can, however, use any
permissible and manageable numbers you wish.
Replacing the variables in the expressions with the numbers picked, you get:
5(3 + 2) − 4(3 + 2) = 25 − 20 = 5.
Then replace the variables in each answer choice to see which choice gives the target number of 5:
(A) (r + s) (t + u)
(5 + 4)(3 + 2) = (9)(5) = 45
Incorrect.
(B) (r − s) (t − u)
(5 − 4)(3 − 2) = (1)(1) = 1
Incorrect.
(C) (r + s) (t − u)
(5 + 4)(3 − 2) = (9)(1) = 9
Incorrect.
(D) (r − s) (t + u)
(5 − 4)(3 + 2) = (1)(5) = 5
Correct!
Step 4: In this example, only choice (D) works. If more than one choice had worked, you would
need to pick another set of numbers and try only those answer choices again.
Not only does Picking Numbers make some problems easier to understand, but also you can be
sure you got the right answer because you’ve already proven the answer works with real numbers.
STRATEGIC GUESSING USING LOGIC
Sometimes, you can determine the characteristics of a correct answer without doing a lot of
calculations. Study the example below.
Question
A er eating 25 percent of the pretzels, Sonya
had 42 le . How many pretzels did Sonya
have originally?
Analysis
Step 1: Original # of pretzels ? 25% of
pretzels = 42.
Step 2: The correct answer represents the
original number of pretzels, before Sonya ate
any.
Question
Analysis
(A) 50
(B) 54
Step 3: Because 25% is the same as onequarter, the correct answer must be divisible
(C) 56
(D) 58
by 4 with no remainder. If the number of
pretzels Sonia started with was not divisible
by 4, and she then ate
of the pretzels, she’d
be le with fractions of pretzels le over.
Of the answer choices, only (C) 56 is evenly
divisible by 4, so it has to be the correct
answer.
Step 4: One-quarter of 56 is 14, and 56 ? 14 =
42, the number of pretzels Sonya had le .
Mark can paint a room in 3 hours, and Kevin can paint an identical room
in 4 hours. How many hours would it take Mark and Kevin to paint the
room if they work together at their respective rates?
(A)
(B)
(C)
(D) 4
Explanation
Step 1: You are told the rates at which two people can paint a room separately.
Step 2: The correct answer represents how long it would take the two people to paint the room
together, each working at the same rate at which he works alone.
Step 3: If Mark, the faster painter, works completely on his own, he will complete the task in 3
hours. With help, he will take even less time to complete the job, so you can eliminate answer
choices (C) and (D), which are greater than 3. Since Kevin is slower than Mark, working together
will take longer than half of 3 hours. Since (A) is half of 3, you can eliminate it. That leaves only
answer choice (B), which must be correct.
Step 4: Check to make sure that the question asked for how long it took to paint just one room. It
did, so (B) is correct.
COMBINATION OF APPROACHES
There is no rule that says you have to use just one approach to get the correct answer. Study the
example below.
Question
Analysis
Youssef can either walk from his home to his
workplace or ride his bicycle. He walks at a
Step 1: The question involves two different
units of time. In order to be able to compare
pace of 1 block per minute, but he can travel
1 block in 20 seconds on his bicycle. If it takes
Youssef 10 minutes longer to walk to work
the rates, first convert Youssef’s biking rate
into minutes. Since a minute is 60 seconds,
he bikes to work at a rate of
, or ,
than to ride his bike, how many blocks away
from work does he live?
minute per block.
He walks to work at 1 minute per block.
Time to walk − time to bike = 10 minutes.
Step 2: The correct answer represents the
number of blocks Youssef lives from his
workplace.
Question
Analysis
(A) 5
(B) 10
Step 3: This problem could be solved with
algebra, but using some logic mixed with
(C) 15
(D) 20
Backsolving can get the correct answer more
quickly.
If Youssef walks 1 block per minute and it
takes him 10 minutes longer to walk than to
ride his bike, the correct answer must be
greater than 10 blocks. Otherwise his bike
time would be zero or less.
That leaves only two choices, 15 or 20, so
pick one and see if it works.
If Youssef lived 15 blocks from work, walking
to work would take him 15 minutes. Riding
his bike at the rate of 20 seconds per block,
he can travel 3 blocks every minute, so he
could ride to work in 15 ÷ 3 = 5 minutes.
Then 15 minutes − 5 minutes = 10 minutes
longer to walk, so 15 is the correct answer.
(Had you chosen to start with 20 instead, you
could quickly have determined that 20 is
incorrect, leaving 15 as the only possible
correct answer.)
Step 4: You tested the correct answer based
on the information given in the question, and
it worked. (C) is correct.
Now, try this one on your own. A combination of strategies may be helpful on this problem.
Shoshanna bought a new cell phone, cell phone case, and wall charger.
The cell phone cost $149.99, the case cost $19.99, and the wall charger
cost $29.99. If tax on each of these items was 9.5%, which of the following
is closest to the total amount Shoshanna spent?
(A) $180
(B) $200
(C) $205
(D) $220
Explanation
Step 1: You are told the prices of three items that Shoshanna purchased, plus a sales tax rate.
Step 2: You are asked to find the answer that is closest to the total amount Shoshanna paid for her
purchases.
Step 3: Because you are asked for the closest amount, you do not have to use an exact calculation
to find the correct answer. Estimation will work well. Round the prices for each item before tax to
the nearest dollar: Shoshanna spent $150 + $20 + $30 = $200 before tax. You can eliminate answer
choices (A) and (B) because they are too small. Now round the tax rate to 10%. Because 10% of
$200 is $20, Shoshanna spent about $200 + $20 = $220 in total. Answer choice (D) is correct.
Step 4: Check that you did the arithmetic correctly and that the answer makes sense. All the other
answer choices are too low to be close to what she spent.
Sometimes, you’ll find that you have to make a guess, but don’t guess at random. Narrow down
the answer choices to increase your odds of guessing the correct one. First, eliminate answer
choices you know are wrong. Next, avoid answer choices that don’t make logical sense. Finally,
choose one of the remaining answer choices.
Math Strategies for the ASVAB
Practice Set
On the ASVAB, either the question itself or the answer choices will
signal which strategy will be most helpful. Look at the partial
questions or answer choices below (note that complete problems
are not shown). Then determine which strategy (Picking Numbers,
Backsolving, Strategic Guessing Using Logic, or a combination of
approaches) is likely to be useful.
1. An airplane uses 79% of a tank of fuel to fly 1,496 miles. If a full tank
holds 996 gallons of fuel, how many gallons would the plane use to
fly 3,016 miles?
Which strategy is likely to be useful for this question, and why?
2.
(A) 80
(B) 100
(C) 120
(D) 150
Which strategy is likely to be useful for this question, and why?
(A)
3.
(B) pb + dc
(C)
(D)
Which strategy is likely to be useful for this question, and why?
4.
(A)
(B)
(C)
(D)
Which strategy is likely to be useful for this question, and why?
5. If
, what is one possible value for x?
Which strategy is likely to be useful for this question, and why?
6. Jim spent 30% of his paycheck on rent, and he spent 40% of the
remainder on car repairs. What percent of his paycheck was le
a er his rent and car repairs?
Which strategy is likely to be useful for this question, and why?
Answers
and Explanations
MATH STRATEGIES FOR THE ASVAB PRACTICE SET
1.
Combination of Approaches This problem includes some unwieldy
numbers, but rounding them for estimation should get you an
approximate answer. Find 80% of 1,000 gallons to determine how many
gallons are used for the first trip (80% × 1,000 = 800 gallons). Then,
round 1,496 to 1,500 and round 3,016 to 3,000. Notice that the question
really asks, “How many gallons of fuel would the airplane use to fly
about twice as far as the first trip?” Just multiply 800 × 2 = 1,600 gallons
and find the answer choice closest to 1,600. In other words, combining a
little calculation with some estimation works well here.
2.
Backsolving Even without a question stem, you can see that all the
answer choices are numbers. That makes this an excellent candidate for
Backsolving. Start by trying (B) or (C).
3.
Picking Numbers There are variables in the answer choices. Picking
Numbers will make the problem more concrete, and plugging the
numbers you picked into the answer choices will allow you to find your
target number.
4.
Strategic Guessing Using Logic Although these fractions might look
intimidating at first, closer examination will show that they are quite
spread out. (A) is very tiny, (B) is about
, (C) is about
, and (D) is close to
. Depending on the question asked, you can probably get a rough idea
of which answer choice is the right answer without doing a lot of
complex calculating.
5.
Backsolving Quickly plug answer choices into the equation to eliminate
choices that are too large or too small.
6.
Picking Numbers A problem with percents and no amount given for
Jim’s paycheck makes this a perfect opportunity for Picking Numbers.
Use $100 for the amount of Jim’s paycheck and then apply the
percentages in the problem. He spends 30% of $100, or $30, on rent.
This leaves him $70, of which he spends 40% on his car, or 40% × $70 =
$28. Subtract $30 for rent and $28 for the car repairs from his $100
paycheck, and he has $42 le . Since $100 represents the full paycheck,
the dollar amount le is the same as the percent le , 42%.
REVIEW AND REFLECT
How did you do? If you weren’t sure which strategy to apply to some of the
partial questions in the practice set, you might want to reread this chapter.
Also, return to it from time to time throughout your ASVAB math practice to
refresh your memory of the various strategies available to you.
The rest of the math section of this book will deal with math content
review. Even if you feel comfortable with a particular subject, make sure to
do the practice sets. There’s no harm in practicing extra problems.
Throughout the math section, you will be given many opportunities to “do
the math.” However, every time you begin a question, first check if you can
use a strategy to minimize your time and effort toward getting the correct
answer. This will allow you to move through the section more efficiently.
Log in to your online resources at kaptest.com/login to watch the video
instruction on strategic approaches to math on the ASVAB.
CHAPTER 6
ARITHMETIC REASONING
Know What to Expect
For the Arithmetic Reasoning (AR) section of the paper-and-pencil ASVAB,
you will have 36 minutes to complete 30 arithmetic word problems. For the
CAT-ASVAB, you will have 42 minutes to complete 15 problems. This
chapter will review the concepts you need to understand in order to
succeed on the Arithmetic Reasoning test. As you work through this
chapter, don’t forget that many problems are best solved by using the
strategies you read about in chapter 5.
The principles covered in this chapter will also serve you well as the
building blocks for Mathematics Knowledge (MK), which will be the focus
of chapter 7. Both the AR and MK subtests are particularly important
because they are part of the AFQT score. Additionally, high AR and MK
scores are required for you to be eligible to enter many of the specialized
occupations in the military.
This chapter will take you through a review of arithmetic concepts
including:
key arithmetic definitions
number properties
absolute value
primes, factors, multiples, and remainders
divisibility rules
fractions, decimals, and scientific notation
exponents and radicals
factorials
The chapter will then review applied arithmetic concepts, such as:
order of operations and calculation rules
ratios, proportions, and rates
combined work
percentages
averages, means, medians, and modes
sequences and probability
The chapter will also discuss Arithmetic word problems including:
translation
word problems with formulas
The chapter concludes with a practice set.
Arithmetic Review
Learning Objectives
In this section, you will learn to:
use the same definitions of key concepts as the ASVAB uses
apply the rules that govern number properties
identify and utilize factors and prime factorization
perform arithmetic operations with decimals, fractions, exponents, radicals, and factorials
convert numbers to and from the scientific notation format
ARITHMETIC DEFINITIONS
It is important that you use certain critical arithmetic terms in exactly the same manner as the ASVAB.
Familiarize yourself with these key terms and concepts.
Concept
Definition
Examples
Integers
All whole numbers, including
zero, and their negative
counterparts.
Fractions
A fraction is a number that is
written in the form
, where A
is the numerator and B is the
denominator.
An improper fraction has a
numerator with a greater
absolute value than that of the
denominator.
A mixed number consists of a
whole number and a fraction.
−900, −3, 0, 1, 54
Concept
Definition
Examples
An improper fraction can be
converted to a mixed number
and vice versa.
Positive/Negative
Numbers greater than 0 are
Positive:
, 1, 5.6, 900
positive numbers; numbers less
than 0 are negative numbers. 0 is
Negative: −64, −40, −1.11,
neither positive nor negative.
Even/Odd
An even number is an integer
that is a multiple of 2. An odd
Even numbers: −8, −2, 0, 12, 188
Odd numbers: −17, −1, 3, 9, 457
number is an integer that is not a
multiple of 2. Fractions and
mixed numbers are neither even
nor odd.
Factor
Prime number
A factor is a positive integer that
The complete list of factors of 12:
divides evenly into a given
number.
1, 2, 3, 4, 6, 12
An integer greater than 1 that
2, 3, 5, 7, 11, 59, 83
has no factors other than 1 and
itself.
2 is the only even prime number.
Consecutive numbers
Multiple
Numbers that follow one a er
another, in order, without
skipping any. In a series of
Consecutive integers: 3, 4, 5, 6
Consecutive even integers: 2, 4,
6, 8, 10
consecutive numbers, the
differences between any
consecutive numbers are equal.
Consecutive multiples of −9: −9,
−18, −27, −36
A multiple of a number is the
Some multiples of 12: 0, 12, 24,
product of that number and an
integer.
60
NUMBER PROPERTIES
Certain number properties follow rules that will never vary. O en, you can use these rules as an effective way
to help you solve problems on the ASVAB.
There are only a few things to remember about positive and negative numbers.
Adding a negative number is the same as subtracting a positive number with the same absolute value.
6 + (−4) is equal to 6 − 4 which equals 2.
4 + (−6) is equal to 4 − 6 which equals −2.
Subtracting a negative number is the same as adding a positive number with the same absolute value.
6 − (−4) is equal to 6 + 4 which equals 10.
−6 − (−4) is equal to −6 + 4 which equals −2.
Multiplying and dividing positive and negative numbers is the same as all other multiplication and division,
with one catch: you need to figure out whether the solution is positive or negative. To do this, count the
number of negative numbers. If you had an odd number of negatives, the answer will be negative. If you
started with an even number of negative numbers, the answer will be positive.
(−6) × (−4)= 24
(2 negatives → positive product)
(−1) × (−6) × (−4) = −24
(3 negatives → negative product)
Similarly,
−24 ÷ 6 = −4
(1 negative → negative quotient)
−24 ÷ (−4) = 6
(2 negatives → positive quotient)
The rules for working with integers are very brief. If you add, subtract, or multiply two integers, the result will
always be an integer. However, if you divide two integers, the result may or may not be an integer.
8 ÷ 4 = 2 which is an integer, but
which is not an integer.
Working with odd and even numbers can be described with a few rules as well. When you add or subtract two
odd numbers or two even numbers, the result will always be an even number.
6 + 4 = 10 (even + even = even)
7 − 3 = 4 (odd − odd = even)
When you add or subtract an even with an odd, the result will be odd.
2 + 7 = 9 (even + odd = odd)
5 − 4 = 1 (odd − even = odd)
When multiplying two numbers, the rule for determining whether the result is even or odd is that any integer
times an even integer will result in an even number. The only way the product of two integers will be an odd
number is if you multiply two odd numbers.
6 × 4 = 24 (even × even = even)
3 × 4 = 12 (odd × even = even)
3 × 5 = 15 (odd × odd = odd)
There are no rules predicting whether the outcome of division will be even or odd because division does not
always result in an integer. Sometimes dividing produces a fraction, and fractions are neither odd nor even.
Study how a well-prepared test taker would apply these rules to an AR question.
Question
If n is an integer, what is 2(n) + 1?
Analysis
Step 1: The question tells you that n is an integer.
Step 2: The question asks for the value of a formula
with a variable, n.
(A) an even integer
(B) an odd integer
(C) an even non-integer
(D) possibly either even or odd
Step 3: Even though you don’t know whether n is
odd or even, it is an integer. When any integer is
multiplied by an even number the result is also an
even number, so the term 2(n) must be even.
If the odd number 1 is added to an even number,
then the result is an odd number. Answer choice
(B) is correct.
Step 4: Check that you used number properties
correctly throughout the problem.
Note that (C) is impossible no matter what the
result of the equation because only integers can be
odd or even.
ABSOLUTE VALUE
When you see a number or expression bracketed by two vertical lines like this |−3|, you are seeing the symbol
for absolute value. The absolute value of what is between the vertical lines is the positive magnitude of the
number, regardless of whether it is positive or negative.
If |x| = 5, then x = ?
Clearly x can equal 5, but x could also equal −5 since absolute value is the positive magnitude of what is
between the vertical lines. Therefore x = +5 or −5.
If |x − 5| = 5, then x = ?
The definition of absolute value says that the expression between the lines can be either 5 or −5. Therefore, in
order to find the possible values of x you must write two equations: x − 5 = 5 and x − 5 = −5
If x − 5 = 5, then x = 10, but if x − 5 = −5, then x = 0. This makes the two possible values of x: 10 and 0.
When you encounter an absolute value problem on the ASVAB you must solve for both the positive and
negative values of whatever is between the vertical lines. Test your understanding of the absolute value
concept on the following problem:
Question
If |x − 2| + 3 = 7 which of the following is a possible
value of x?
Analysis
Step 1: The question gives you a formula with
variable x.
Step 2: The question asks for one possible value of
x.
Question
(A) 6
(B) -6
(C) 2
(D) 4
Analysis
Step 3: First, subtract 3 from both sides.
|x − 2| + 3 = 7 becomes
|x − 2| = 4.
Thus, x − 2 must equal either +4 or −4.
If x − 2 = 4, then x = 6
If x − 2 = −4, then x = −2.
Since −2 is not among the answer choices, (A), 6, is
the only correct choice.
Step 4: Check your math and check to make sure
you solved for the proper variable. In this case, the
only variable was x, but other problems might
contain more than one variable and require you to
choose correctly.
FACTORS, MULTIPLES, AND PRIME NUMBERS
In order to determine the factors of a number, find the pairs of positive integers which can be multiplied
together to produce the number that is being factored. Start with 1 and the number itself, which are always
factors of any integer. Then examine 2, 3, 4 and so on, as shown in this example of finding the factors of 36: 1 ×
36
2 × 18
3 × 12
4×9
6×6
Examining the two columns shows that the factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, and 36. When creating the list
of factors, as soon as you reach a factor on the le which is equal to or greater than a factor already listed on
the right, you can stop, since you’re about to start repeating factor pairs. In this table, you need go no higher
than 6 because any number greater than 6 that is a factor of 36 is already in the right column.
Multiples are, in a way, the opposite of factors. For instance, in the example above, 1, 2, 3, 4, 6, 9, 12, and 18
are factors of 36. Conversely, 36 is a multiple of 1, 2, 3, 4, 6, 9, 12, and 18.
If you become confused between the terms factor and multiple, you can remember that multiples are larger
because you can produce them by multiplying. There are a finite number of factors of any number, but there
are an infinite number of multiples.
Prime numbers, by their very definition, cannot be multiples of any integers other than 1 and the prime
number itself. However, prime numbers can be factors of other numbers.
3 × 13 = 39 (3 and 13 are prime numbers, but 39 is not because it is a multiple of 3 and a multiple of 13.) A
number’s prime factors are factors that are prime. The prime factorization of a number is the number
expressed using multiplication containing only primes, even if some of those primes repeat.
To determine the prime factorization of a number, keep dividing by prime numbers until you can no longer
divide because you are le with only prime numbers.
For example, to find the prime factorization of 168:
Since 168 is an even number, the prime number 2 is a factor of 168.
168 = 84 × 2, so 2 is a prime factor of 168.
84 is still an even number equal to 42 × 2, so 2 is a prime factor for a second time.
42 is still an even number equal to 21 × 2, so 2 is a prime factor for the third time.
21 is the product of 3 and 7.
Since these are both prime numbers, the process of finding the prime factors is complete.
An efficient way to determine the prime factors of any number is to use a “tree” as shown below.
Based on the above operations and tree, the prime factorization of 168 is 2 × 2 × 2 × 3 × 7. All the prime factors,
including repeated numbers, must be listed because the original number is the product of all of these
numbers.
Prime factorization can be a very useful tool to help answer some questions on the ASVAB. For instance, if you
need to find the greatest common factor (GCF) of two integers, break down both integers into their prime
factorizations and multiply all prime factors they have in common, as shown in the example below:
Question
Find the greatest common factor of 40 and 140.
Analysis
Step 1: You are given two numbers, 40 and 140.
Step 2: The question asks for the greatest common
factor of the two numbers.
Step 3:
The prime factors of 40 are 2, 2, 2, and 5.
The prime factors of 140 are 2, 2, 5, and 7.
Both numbers share two 2s and a 5 as prime
factors, so the GCF is 2 × 2 × 5 = 20.
Step 4: Double-checking the result, 40 = 20 × 2 and
140 = 20 × 7.
This can be helpful when you need to reduce a fraction, because you can find the GCF and then divide the top
and bottom of the fraction by that number.
If you need to find a common multiple of two integers, you can just multiply them. However, in other cases
you may need to find the least common multiple (LCM). You can use prime factors to efficiently identify LCMs.
Take a look at this example to see how that works.
Question
Find the least common multiple of 20 and 16.
Analysis
Step 1: You are given two numbers, 20 and 16.
Step 2: The question asks for the least common
multiple of the two numbers.
Question
Analysis
Step 3:
First, identify the prime factors of each number:
16 = 2 × 2 × 2 × 2
20 = 2 × 2 × 5
Any integer that is a multiple of 16 must have four
prime factors of 2. Any integer that is a multiple of
20 must have two prime factors of 2 and one prime
factor of 5.
Therefore, any number that is a multiple of both 16
and 20 must have four prime factors of 2 and one
prime factor of 5.
The least common multiple equals
2 × 2 × 2 × 2 × 5 = 80.
Step 4: Double-check that all of the prime factors
for each number were included in the least
common multiple.
Practice the technique on this question:
Marcus needs to order some parts for his machine shop. His supplier sometimes
fills orders with boxes that contain 15 of these parts and sometimes with boxes of
18, depending upon what he happens to have in stock. The supplier will only ship
complete boxes, and will ship only one size of box in a given order. What is the
minimum quantity of parts that Marcus can order and be assured that he will
receive exactly that many parts regardless of which boxes his supplier uses?
(A) 15
(B) 18
(C) 90
(D) 270
Explanation
Step 1: The question gives you a situation in which Marcus is ordering parts. He wants to receive the exact
number of parts he needs. You are told that the company ships parts in boxes of 15 and 18.
Step 2: You are asked to find the smallest number of parts that can be filled with full boxes of 15 parts or full
boxes of 18 parts. Thus, you need to find the least common multiple of 15 and 18.
Step 3: The prime factors of 18 are 2 × 3 × 3 and the prime factors of 15 are 5 × 3. Therefore, the least common
multiple must have two factors of 3, one factor of 2, and one factor of 5. This is 2 × 3 × 3 × 5 = 90. Answer choice
(C) is correct.
Notice that (D), 270, is a common multiple of 15 and 18, but it is not the least common multiple.
Step 4: Confirm that 15 and 18 both divide evenly into 90.
DIVISIBILITY
Whether evaluating integers to determine if they are prime numbers, finding factors, or finding prime factors,
you can check whether a number is a factor of another number more quickly and effectively if you use the
following tips to check for divisibility.
Divisibility Rules
Number
Divisibility Rule
2
All even numbers are divisible by 2.
3
Add up the individual digits of the number. If the total is divisible by 3, then the number itself is divisible by 3; for example, 243 is
divisible by 3 because the sum of its digits is 2 + 4 + 3 = 9, but 367 is not because the sum of its digits is 3 + 6 + 7 = 16 and 16 is not a
multiple of 3.
4
Take the last two digits and divide them by 2. If the result is even, the number is divisible by 4. If the result is odd, then the number
is not divisible by 4.
5
All numbers ending in 5 or 0 are divisible by 5.
6
All even numbers that meet the test for divisibility by 3 are divisible by 6.
8
Divide the number by 2 twice; if the result is even, then the number is divisible by 8.
9
Add up the digits of the number; if the total is divisible by 9, then the number is divisible by 9.
Practice divisibility rules on this question:
Question
What are all the prime numbers between 60 and 70
inclusive?
Analysis
Step 1: You are given a range of numbers.
Question
Analysis
Step 2: The question asks for the number of primes
within a given range.
(A) 61, 67
Step 3:
(B) 61, 63, 67
Use divisibility tests to eliminate numbers that are
not prime.
(C) 61, 63, 65, 67
Eliminate 60, 62, 64, 66, 68, and 70 because they
(D) 62, 64, 66, 68
are all divisible by 2.
Eliminate 65 because it is divisible by 5.
Checking for divisibility by 3 eliminates 63 (sum of
the digits is 9) and 69 (sum of the digits is 15).
The only remaining numbers are 61 and 67. Answer
choice (A) is correct.
Step 4: All of the other answer choices contain
numbers that were eliminated by using divisibility
rules.
FRACTIONS AND DECIMALS
Generally, it’s a good idea to reduce fractions when solving math questions. To do this, use your knowledge of
factors to cancel all factors that the numerator and denominator have in common.
When you perform operations on fractions, always remember to perform the same operation on both the
numerator and the denominator. For instance, in the example above, both the numerator and denominator
were divided by 4.
To add or subtract fractions, you must convert all the fractions so that they have a common denominator.
Think of the process of converting to a common denominator as finding the least common multiple of all the
denominators. Don’t forget to multiply the individual numerators by the same number that was used to
convert to a common denominator. Once you have converted the individual fractions so that they have
common denominators, you merely add or subtract the numerators to obtain your result.
To multiply fractions, multiply the numerators together and then multiply the denominators together.
To divide one fraction by another you invert (flip) the second fraction and multiply. In other words, multiply
the first fraction by the reciprocal of the second fraction.
Occasionally a question may require that you compare fractions to determine which has the greater value.
The most straightforward way to do this is to convert the fractions being compared to a common denominator
and compare their numerators.
Question
Compare
and
.
Analysis
The lowest common denominator is 3 × 8 = 24.
Multiple the first fraction by
fraction by
.
16 is greater than 15, so
Practice the operations for fractions to answer the following question:
=?
and the second
is greater than
.
(A)
(B)
(C)
(D)
Explanation
Step 1: You are given an equation.
Step 2: You need to solve the equation using fraction rules.
Step 3: Dividing by a fraction is the same as multiplying by its reciprocal, so you can get rid of the cumbersome
double-stack fraction by rewriting:
You need to add the two fractions in the le parentheses before multiplying. In order to add the two fractions,
convert them to have a common denominator of 20.
Now add the first two fractions.
Multiplying the numerators and denominators results in an answer of
. But this answer is not in the
answer choices as written. For this problem, you must convert an improper fraction to a mixed number.
. Select answer choice (C).
Step 4: Check to be sure you used the proper order of operations and check your math.
To convert a fraction to a decimal, divide the denominator into the numerator.
To convert
to a decimal, divide 25 into 8.
To convert a decimal to a fraction, first set the decimal as the numerator of a fraction with a denominator of
1. Then, move the decimal over as many places as it takes until it is immediately to the right of the units digit.
Count the number of places that you moved the decimal. Then add that many 0s to the 1 in the denominator.
Try this one on your own:
0.0025 = ?
(A)
(B)
(C)
(D)
Explanation
Step 1: The question gives you a number in decimal format.
Step 2: The answer choices show you that you will need to convert to a fraction.
Step 3: First, convert to a fraction with a denominator of 1,
. In order to get rid of the decimal in the
numerator, you will need to move it four places to the right and simultaneously add four 0s to the
denominator. This results in the fraction
.
To reduce this fraction to its simplest terms, divide both the numerator and denominator by 5 to get
Since both the numerator and denominator are still divisible by 5, repeat the process to get
.
. Select
answer choice (B).
Step 4: Since many of the answer choices vary by the number of zeros in the denominator, double-check that
you added the appropriate number of zeros to the denominator before you started simplifying.
DECIMAL DIVISION
One common type of arithmetic problem on the ASVAB involves dividing numbers that contain decimals.
Keeping track of the decimal places can complicate a division problem, so get rid of the decimal places before
you divide. You can accomplish this by multiplying both numbers by 10 as many times as necessary. When you
multiply a number with decimals by 10, simply move the decimal point one place to the right. When
multiplying numbers without decimals by ten, add a zero at the end.
As an example,
1.22 × 10 = 12.2
12.2 × 10 = 122
122 × 10 = 1,220
When presented with a decimal division question you should write the division problem as a fraction:
Then you will move the decimal points in the denominator and the numerator the same number of places to
the right, adding zeros as necessary, until you have completely gotten rid of any decimal points.
The example below shows how to tackle an ASVAB question about decimal operations.
Question
David is drawing a blueprint for a model home. Due
to the scale he used, the width of the bathroom
Analysis
Step 1: You are told that there are 0.18 inches to
draw 30 tiles.
floor is 0.18 inches on his paper. He needs to draw
30 tiles across that width. What is the width of each
individual tile in his sketch in inches?
Step 2: The question asks for the measurement of
width in inches of each tile as drawn on the paper.
Question
Analysis
(A) 0.006
Step 3: You need to divide 30 into 0.18.
(B) 0.06
(C) 0.6
(D) 6
Write the problem as a fraction:
. Eliminate
the decimal point by moving it two places to the
right and adding 2 zeros to the denominator:
.
A quick glance at the answer choices reveals that
they are in decimal format rather than fractions, so
you need to convert to a decimal.
Divide both the numerator and denominator by the
common factor of 3 so that the numbers are easier
to work with:
.
You have to get rid of the 3 zeros in the
denominator so that the denominator becomes 1.
Move the decimal point in the numerator 3 places
to the le , inserting zeros a er the decimal as
needed, resulting in
. Answer
choice (A) is correct.
Step 4:Check your math carefully. Double-check
that you inserted the correct number of zeros.
Scientific notation is a method of writing very large and very small numbers that also involves moving
decimal points. The first part of a number in scientific notation will be equal to or greater than 1 and less than
10. The second part of the number will be a power of 10. For powers of 10, the exponent is the number of
zeroes the number has when written out. For example, 104 = 10,000. For numbers written in scientific notation,
where the first number always has exactly one digit to the le of the decimal point, the long version of the
number can be written out by moving the decimal to the right by the same number of places as the value in
the exponent of the power of 10.
1.23 × 104 = 12,300
Scientific notation also uses negative exponents to indicate the proper placement of the decimal point in a
very small number. A negative exponent in scientific notation means that you move the decimal point to the
le . Once the decimal point has been moved as far le as possible, start adding zeros to the right of the
decimal.
4.321 × 10−2 = 0.04321
Use this problem to practice your understanding of scientific notation:
Question
Sam writes for a scientific journal. In her research,
Analysis
Step 1: You are given a number.
she finds a number written as 6,483,000. How can
she express that in scientific notation?
Step 2: You are asked to rewrite the number in
scientific notation.
(A) 6.483 × 103
Step 3: Move the decimal point 6 places to the le
so 6,483,000 becomes 6.483000.
(B) 6.483 × 105
If you move the decimal 6 places to the le , you
(C) 6.483 × 106
must write 106.
(D) 6.483 × 107
Thus, written in scientific notation the number
becomes (C) 6.483 × 106.
Step 4: Check to be sure you moved the decimal
over the correct number of places.
EXPONENTS AND RADICALS
Exponents are the small raised numbers written above and to the right of a variable or number (the base).
They indicate the number of times that the variable or number is multiplied by itself. The rules for performing
different operations on terms involving a base and an exponent will require you to pay close attention to the
details. There are two important things to remember about exponents. First, any number or variable with an
exponent of 1 is equal to the base itself. Second, any number or variable with an exponent of 0 equals 1.
x1 = x
51 = 5
x0 = 1
50 = 1
To add or subtract terms involving variables and exponents, both the variables and the exponents must be the
same.
2x2 + x2 = 3x2
3x4 − 2x4 = x4
x2 + x3 cannot be combined.
a2 + b2 cannot be combined.
To multiply terms with the same base, merely add the exponents. This can be done because exponents
represent how many times the base is multiplied by itself.
23 × 22 = (2 × 2 × 2) × (2 × 2) = 23+2 = 25
Similarly, to divide terms with the same base, subtract the exponent that is in the denominator from the
exponent in the numerator.
To raise a term involving an exponent to another exponent, multiply the exponents.
(x2)4 = x2×4 = x8
A coefficient is a number multiplied by a variable in a term. For instance, in the term 2x², the coefficient is 2. To
multiply terms consisting of coefficients and exponents that have the same variable in the base, multiply the
coefficients and add the exponents.
6x7 × 2x5 = (6 × 2) (x7+5) = 12x12
To divide terms consisting of coefficients and exponents that have the same variable in the base, divide the
coefficients and subtract the exponents.
6x7 ÷ 2x5 = (6 ÷ 2) (x7−5) = 3x2
You might see a negative exponent in a problem on the ASVAB. Don’t panic! Negative exponents are just the
reciprocal of their positive counterparts.
Practice working with exponents on this problem:
Question
Analysis
Step 1: You are given an equation.
Step 2: You need to simplify the equation.
Question
Analysis
(A) n8
Step 3: Since there are variables in the question
(B) 2n8
stem and the answer, you can use Picking Numbers
here.
(C) 3n8
Pick a number for n and solve for the equation in
(D) n20
the question stem. The result is your target
number.
Then plug your initial number for n into all of the
answer choices and the one that yields the target
number would be correct.
To solve with straightforward math, apply the
exponent rules one at a time.
Using the rule for multiplying two terms with the
same base (in this case, n) the numerator of the
first expression can be simplified to read:
. Next, apply the rule for
division of terms with the same base so that the
expression on the le becomes:
.
Use the rule for raising an exponent to an exponent
and you have
.
A number to a negative exponent is the same as the
reciprocal of that number to a positive exponent.
Thus, the expression on the right can be rewritten
as: n8 + 2n8.
Since both terms have the same base and the same
exponent, you can add them together to get the
correct answer, 3n8, choice (C).
Question
Analysis
Step 4: Briefly confirm that you performed the
steps correctly.
Try this problem both by Picking Numbers and by using straightforward math so that you get a sense of which
method you will be more comfortable with for this type of problem on Test Day.
Perfect squares are integers that are the result of squaring (multiplying by itself) another integer. For
instance, 25 is a perfect square because it is 5 × 5. You can save time and trouble on the ASVAB if you memorize
the perfect squares up through 12 × 12 = 144.
Hone your skills with the following practice problem:
Question
Analysis
Which of the following numbers is NOT a perfect
Step 1: The question stem doesn’t give much
square?
information, but you can infer that three of the
answer choices ARE perfect squares.
Step 2: You are looking for a number that is not
equal to an integer times itself.
(A) 1
Step 3:
(B) 16
1 = 1 × 1, so it is a perfect square.
(C) 27
16 = 4 × 4, which is also a perfect square.
(D) 36
27 = 3 × 3 × 3, which is not a perfect square because
it is a number multiplied by itself three times rather
than twice.
Answer choice (C) is correct.
Step 4: Check to see if the remaining answer
choice is a perfect square.
36 = 6 × 6, so it is a perfect square.
A square root is a number that, when multiplied by itself, produces the given quantity. The radical sign is used
to represent the positive square root of a number, so
, since 5 × 5 = 25. (Even though (−5) × (− 5) is
also 25, when you are asked for the square root, the answer will be a positive number.) To add or subtract
radicals, make sure the numbers under the radical sign are the same. If they are, you can add or subtract the
coefficients outside the radical signs.
cannot be combined.
To simplify radicals, factor out the perfect squares under the radical, calculate the square roots of the perfect
squares, and put the results in front of the radical sign.
Note that when you have simplified to the point where the number under the radical does not contain any
perfect squares, your result will be sufficient for the ASVAB.
To multiply or divide radicals, multiply or divide the coefficients outside and inside the radical separately.
To take the square root of a fraction, you can break the fraction into two separate roots and take the square
root of the numerator and the denominator separately.
Practice computations with radicals on this problem:
Question
Simplify
Analysis
Step 1:The question gives an expression in the
form of a fraction.
Question
Analysis
Step 2: You are asked to simplify the fraction as
much as possible.
Question
(A)
Analysis
Step 3: First, check to see if there is anything you
can divide out of the top and bottom to make the
fraction easier to work with.
(B)
(C)
(D)
In this case, there is not. Since the example
contains a radical sign, check to see if any of the
numbers (as written) are perfect squares.
None of the numbers are perfect squares, so
complete the multiplication on the top and on the
bottom.
Before performing the division, check to see if any
of the numbers are perfect squares.
81 = 9 × 9
64 = 8 × 8
Since both numbers are perfect squares, take the
square root of the top and bottom independently.
Scanning the answer choices,
is not present as
written. However, since the numerator is greater
than the denominator, this is an improper fraction
that can be converted to a mixed number.
Answer choice (C) is correct.
Question
Analysis
Step 4: Check your math and check to be sure you
solved for the correct question.
FACTORIALS
On the ASVAB math sections, you may see an occasional factorial question. You’ll know you’re dealing with a
factorial when you see an integer followed by an exclamation point (!). A factorial is the product of the integer
before the factorial sign and all the positive integers below it. For instance, when you see the following: 7! = ?
The question is actually asking you what “7 factorial” is, and the answer to that question is: 7! = 7 × 6 × 5 × 4 × 3
× 2 × 1 = 5,040
If you’re ever given a fraction with factorials, there’s o en a lot of canceling that you can do before you try to
multiply out the factorials.
Look at the following example.
Question
Solve for
.
Analysis
Step 1: You are given a fraction containing
factorials.
Step 2: You need to perform the calculations.
Step 3: Write out the factorials
Cancel out the numbers that appear on the top and
bottom.
The correct answer is 30.
Step 4: Double-check your calculations and your
elimination.
If you see a problem with factorials in a fraction on Test Day, simplify before attempting to solve.
Log in to your online resources at kaptest.com/login to watch the video instruction on every Arithmetic
Reasoning topic in this section. If you haven’t yet registered your book, see “Welcome to Your ASVAB Studies”
toward the front of this book for registration instructions.
Applied Arithmetic Review
Learning Objectives
In this section, you will learn to:
calculate values for complex arithmetic expressions using the proper
rules and order of operations
utilize ratios, percentages, and proportions to solve problems involving
comparisons
solve rate and work problems
apply the formulas for statistical terms to different situations
compute numerical probabilities
While the arithmetic concepts you’ve looked at so far could appear on the
Arithmetic Reasoning section of the ASVAB, it’s worth noting that, due to the very
nature of word problems, most of the questions in this section will involve some
form of applied arithmetic. On the ASVAB you will use arithmetic principles to solve
practical problems. Applied arithmetic includes subjects like ratios, percent
problems, rates, averages, and probability.
THE ORDER OF OPERATIONS
You must perform arithmetic operations in the proper order to get the correct
answer to complex arithmetic problems. The acronym PEMDAS can help you
remember that order.
P = Parentheses
E = Exponents
M D = Multiplication and Division (from le to right) A S = Addition and
Subtraction (from le to right) For example:
One way to remember PEMDAS is to think of the phrase “Please Excuse My Dear
Aunt Sally.”
Try out PEMDAS on this problem:
Question
Solve 3 × 5 + (6 × 2) − 33.
Analysis
Step 1: You are given an equation.
Step 2: You are asked to solve that
equation.
Question
Analysis
Step 3:
Use PEMDAS:
3 × 5 + (6 × 2) − 33
(P) 3 × 5 + 12 − 33
(E) 3 × 5 + 12 − 27
(MD) 15 + 12 − 27
(AS) 0
Step 4: Double-check that you
performed the operations in the
correct order and that your math
calculations were performed
correctly.
DISTRIBUTIVE AND COMMUTATIVE PROPERTIES
In addition to being certain to follow the correct order of operations when solving
complex arithmetic problems, you may find that you need to utilize the distributive
and commutative properties of mathematics to facilitate your computations. It’s
not important that you remember the specific terms “distributive” and
“commutative,” but it is important that you know how to use these properties.
The distributive property says that the result of multiplying one number by the
sum or difference of two numbers can be obtained by multiplying each number
individually and then totaling the results.
5 × (20 + 2) = 5 × 20 + 5 × 2 = 100 + 10 = 110
5 × (20 − 2) = 5 × 20 − 5 × 2 = 100 − 10 = 90
Similarly, a fraction with multiple terms in the numerator and only one term in the
denominator can be subdivided.
Do not attempt to use this property if the denominator has more than one term.
cannot be split up.
Not only is the distributive property useful in solving problems on the ASVAB, it can
also help you quickly and accurately multiply in the absence of a calculator.
Question
Multiply 6 × 38 without a calculator.
Analysis
You can convert that to 6 × (30 + 8).
Then, 6 × 30 + 6 × 8 = 180 + 48 = 228.
Try this sample problem:
(A) 10x + 34
(B) 10x + 136
(C) 12x + 134
(D) 12x + 136
Explanation
Step 1: You are given an equation.
Step 2: You are asked to solve that equation.
Step 3: You can simplify multiplying 17 × 8 by treating that as (10 + 7) × 8 = 80 + 56 =
136.
The fraction is equivalent to
.
Now the simplified expression is 136 + 12x − 2 = 12x + 134. Answer choice (C) is
correct.
Step 4: Check your math and make sure you used the correct order of operations.
The commutative property says, in a nutshell, that order does not matter when
adding or multiplying numbers. For example: 3 × 4 = 4 × 3
3+4=4+3
This property does not change PEMDAS; it merely gives you some flexibility when
you get to the multiply or add part of the order of operations. The commutative
property does not apply to subtraction or division.
4 − 3 does not equal 3 − 4.
does not equal
.
This flexibility when dealing with addition and, in particular, multiplication can be
a handy addition to your arithmetic toolbox as shown in the example below:
Question
Solve for 2 × 19 × 5 without a
Analysis
Step 1: You are given an equation.
calculator.
Step 2:You need to solve this
equation without a calculator.
Step 3: You could answer this by first
multiplying 2 × 19 = 38, then
multiplying 38 × 5 = 190.
However, before jumping straight
into the math, use strategic logic.
Note that 2 × 5 = 10. This is helpful
because 10 is an easy number to
multiply.
If you rearrange the equation as 2 × 5
× 19 before solving, the math
becomes more manageable.
2 × 5 × 19 = 10 × 19 = 190
Step 4: Double-check your math.
RATIOS, PROPORTIONS, AND RATES
Ratios represent the relationship of one quantity to another. Ratios can be
presented in three different ways. They can be verbal, such as “the ratio of cats to
dogs is 3 to 4.” Another way of describing a ratio is to use a colon, as in “3:4.” In
order to use ratios in calculations, however, you will use the fractional form,
.
Ratios do not necessarily represent the actual number of two different things. In
this example, you don’t know if there are actually 3 dogs and 4 cats, or 6 cats and 8
dogs, or 600 cats and 800 dogs.
Ratios are either part to part or part to whole relationships, depending upon
what quantities are being compared: A class contains 12 male students and 21
female students.
The part to part ratio of male students to female students is
The part to whole ratio of male students to all the students in the class is
Always simplify ratios to their lowest terms, as was done in the above example.
Here’s how an expert test taker would apply these basic rules for ratios to an AR
question:
Question
Analysis
Question
Analysis
Alicia is an avid video game player.
Step 1: The question gives the total
She has a total of 21 video games.
Her ratio of sports games to action
games to mystery games is 4:2:1.
number of video games and the ratio
of different types of games in the
collection.
How many action games does she
have?
Step 2: The question asks for the
number of action games in the
collection.
(A) 2
Step 3: The part to whole ratio of
action games to total video games
(B) 6
can be represented as
.
(C) 8
But Alicia has a total of 21 games, not
(D) 12
7.
In order to determine how many
action games Alicia has, multiply the
part to whole ratio by the total
number of games:
.
Answer choice (B) is correct.
Question
Analysis
Step 4: You can double-check that
does, in fact, equal the part to
whole ratio of
by dividing the
numerator and denominator by their
lowest common multiple, which is 3.
A proportion is an equation of two ratios that shows the comparative relationship
between parts, things, or elements with respect to size, amount, or degree.
When working with proportions, you can use a helpful technique called crossmultiplying to help solve the equation. To cross-multiply an equation that consists
of two fractions, you multiply the numerator of the first fraction by the
denominator of the second and vice versa. Here is an example of cross-multiplying:
2x(4)=3(5)
Here’s an example of a proportion question in which you can use crossmultiplying:
Question
Analysis
Question
Analysis
A picture that is 4 inches wide and 6
Step 1: The question gives you the
inches long is enlarged so that it is
dimensions of a picture and says that
the picture was then enlarged.
inches long.
What is the width of the enlarged
picture?
Step 2: The question asks for the new
width of the picture.
Question
Analysis
Step 3: Set the given information up
as a proportion. The ratio of width to
length in the original picture is 4:6
and the ratio of width to length of the
enlargement will be the same.
The length of the enlargement will be
inches, but the width is some
unknown value (w). Since the
width/length ratio of the two pictures
must be the same, you can set the
proportions equal to each other:
So, the enlarged picture is 5 inches
wide.
Step 4: Double-check your math.
Also, be sure you put the correct
measurements in the correct places
in the ratio.
Practice working with ratios on this sample problem:
Micah can ride his bicycle 42 miles in 3 hours. Assuming that
he travels at the same speed, how long would it take Micah
to ride 70 miles?
(A) 5.0 hours
(B) 5.5 hours
(C) 7.0 hours
(D) 7.5 hours
Explanation
Step 1: The problem states that Micah rides at the same speed in both instances.
You are told how long it takes to ride 42 miles.
Step 2: You are asked how long it will take him to ride 70 miles.
Step 3: Micah’s distance to time relationship can be set up using a proportion.
Using the cross-multiplication technique,
.
Before multiplying large numbers together and then dividing by 42, check to see if
you can reduce the equation. Since 42 is a multiple of 3, you can divide both sides
of the equation by 3.
70 = 14t
5=t
Answer choice (A) is correct.
Step 4: You can double-check your math by inserting your answer into the
proportion and cross-multiplying.
3(70) = 5(42)
210 = 210
A rate is simply a ratio that compares two different but related quantities, such as
distance divided by time (speed), or amount divided by time, or cost per unit.
In other words:
or
or
Another way to look at rates is to think of them as changes in the numerator per
changes in the denominator. For instance, if your rate of pay is $15/hour, you know
that if you work one more hour you will earn an additional $15.
The key to solving rate problems is to set them up as proportions. Convert the units
if necessary and solve for the unknown value.
Take a look at the following rate question:
Question
Analysis
Question
Analysis
A waitress serves 3 diners every 5
minutes. At this rate, how many
customers will she serve in one hour?
Step 1: The question gives the rate at
which a waitress can serve people.
The rate is given in minutes.
Step 2: The question asks for the
number of customers that will be
served in one hour.
Step 3:
Set the rate up as a proportion.
Convert units.
Cross-multiply and solve.
5x = 180
x = 36
Question
Analysis
Step 4: Double-check your math and
that the units were converted
correctly.
Pay close attention to units in ratios and proportions. Had hours not been
converted to minutes in the example, the answer would have been wrong.
Try this sample problem to practice rates and units:
The volume of a certain substance is directly proportional to
its weight. If 48 cubic inches of the substance weigh 112
ounces, what is the volume, in cubic inches, of 63 ounces of
the substance?
(A) 27
(B) 36
(C) 42
(D) 64
Explanation
Step 1: The problem gives the ratio of volume to weight of a certain substance.
Step 2: The problem asks for the volume of a different amount of the substance.
Step 3: Start by setting up the proportion
.
You might notice that cross-multiplying this proportion looks difficult without a
calculator and wonder if there is a more efficient way to answer the question.
There is, by using logic.
In the given ratio, 48 is less than half of 112, so the correct answer will be less than
half of 63. Looking at the answer choices, only 27 is less than half of 63.
Answer choice (A) is correct.
Step 4: You can double-check your work by reducing the proportions to their
lowest form and checking that they equal each other.
Both proportions reduce to
, which means that the two proportions are equal
and the answer choice is confirmed.
COMBINED WORK
You may see a problem on the ASVAB that asks you to determine how long it takes
the combined effort of two people or machines to complete a task, or something
similar such as how long it takes for two pipes to fill a tank.These are just a
different form of rate problem.
For instance, if it takes Joe 3 hours to paint a room, then his rate of painting is
. The tasks to be completed that are on the ASVAB are additive; the
combined work of the people (or machines or pipes) can be added together to
obtain a combined rate. This approach also works for more than two entities
working on the same task.
Question
Analysis
Jose can paint a room in 3 hours. Jill
can paint the same room in 2 hours.
How long will it take them to paint
Step 1: The question gives the
amount of time it takes two different
people to paint a room.
the room working together?
Step 2: The question asks for the
length of time it will take them to
paint the room together.
Question
Analysis
Step 3:
Express the individual times as rates.
Convert to a common denominator
and add the rates.
Invert the fraction.
If it takes 6 hours to paint 5 rooms, it
would take
hours to paint 1 room.
Step 4: Double-check your math.
Also double-check that you are
solving for the correct number of
rooms, in this case, 1 room.
Try this problem (which does not have answer choices) on your own:
There are three pipes that can be used to fill a tank. One of
them can fill the tank in 2 hours, another can fill it in 3 hours,
and the third can fill the tank in 6 hours. If all three pipes are
used to fill the tank simultaneously, how long will it take?
Explanation
Step 1: The three times needed for each pipe to fill the tank individually are given.
Step 2: You are asked to calculate the rate at which they would be able to fill the
tank together.
Step 3: The rates can be converted to
, specifically
,
, and
.
Convert their rates to a common denominator and add:
. Therefore to fill the one tank, the three
pipes working together can accomplish the task in 1 hour.
PERCENT PROBLEMS
Percents are ratios of an amount to 100, so the techniques used to work with ratios
and proportions are valuable tools when you work with percents.
Question
A bag contains 8 marbles and 6 of
them are green. What percent of the
marbles in the bag are green?
Analysis
Step 1: The question gives the total
amount of marbles and the amount
of green marbles.
Question
Analysis
Step 2: The question asks for the
percent of total marbles that are
green.
Step 3: To solve this, you can set up a
proportion equating the numbers of
marbles to the unknown percentage:
600 = 8g
75 = g
So 75% of the marbles are green.
Step 4: Double-check to confirm your
math is correct.
To convert the English into math on a percent problem, use the following
conversion table.
English
Math Translation
% or percent
÷ 100 (or use decimal or fractional equivalent)
of
× (times)
what
x (or n, or any variable you like)
is
= (equals)
Using these translations, you can see, for instance, that 40% of 25 = 0.40 × 25 = 10.
Some ASVAB questions require you to increase or decrease a number by a given
percent. To calculate such increases or decrease, take that percent of the original
number and add it to or subtract it from the original number.
To increase 25 by 60%, first find 60% of 25.
25 × 0.6 = 15
Then add the result to the original number.
25 + 15 = 40
To decrease 25 by the same percent, subtract the 15.
25 − 15 = 10
Other ASVAB questions, rather than giving you the percent increase or decrease,
will ask you to calculate the percentage change between an original value and a
new value. In order to calculate that change, always use this formula: Percent
Change = 100% ×
If the percent change is an increase, the result will be positive. If the change is a
decrease, the result will be negative. ASVAB percentage change problems ask for
the change relative to the original value; using the new value in the denominator
will produce an incorrect answer.
Question
Analysis
Question
Analysis
A camera that originally cost $125
was sold on sale for $100. The sale
Step 1: The question gives the
original price and the sale price of a
price was what percent less than the
original price?
camera.
Step 2: The question asks for the
percentage decrease between the
sale price and the original price.
Step 3: Percent Change = 100% ×
= 100% ×
×
= 100%
= −20%
Since the result is negative, you know
that there was a price decrease. The
answer is −20%.
Step 4: Briefly confirm that the
answer makes sense. 20% of 125 is
25, so your answer is correct.
Practice using the formula on this sample problem:
Ryan weighed 40 pounds when he finished kindergarten and
44 pounds when he started first grade. What was the
percentage change in his weight between kindergarten and
first grade?
(A) 10% decrease
(B) 4% increase
(C) 10% increase
(D) 40% increase
Explanation
Step 1: The problem gives Ryan’s weight at various ages.
Step 2: The question asks for his percent change in weight.
Step 3:
Percent Change = 100% ×
= 100% ×
= 100% ×
= 10%
Since the result is positive, the answer is a 10% increase, choice (C).
Step 4: Check your calculations and check that you solved for the percent asked
for.
Now practice this skill on another problem.
Rachel made a certain investment in the stock market but the
value of her investment declined by 20%. However, the value
of that investment then increased by 50%. What was the
overall percentage change in the value of the investment
from the original purchase price?
(A) 30% decrease
(B) No change
(C) 20% increase
(D) 30% increase
Explanation
Step 1: The question gives information about the decrease and increase in the
value of a stock.
Step 2: The question asks for the overall change.
Step 3: Notice that the question does not mention any specific prices. That makes
this problem an excellent candidate for the Picking Numbers technique. Since the
problem deals with percentages, start with an original value equal to 100.
If the investment lost 20% of its value, that would have been a loss of 20, so the
value a er the decrease would have been 80. Fortunately for Rachel, the value then
increased 50%. Since the 50% increase was based upon a value of 80, that would
be a gain of 40. This results in a final value of 80 + 40 = 120, which is a 20% increase
from the original assigned value of 100, answer choice (C).
Step 4: Confirm that your math is correct and that you are solving for the correct
piece of information.
STATISTICAL TERMS
Averages, like ratios, proportions, and rates, use fractions to find the answer to a
problem. Here is the average formula:
What is the average of 3, 4, and 8?
Sometimes the ASVAB may not present the information in such simple terms. The
formula for averages, like other three-part formulas, can be rearranged as needed.
Question
Six people went fishing and caught
an average of 7 fish each. How many
total fish did they catch?
Analysis
Step 1: You are given the average
amount of fish caught by 7 people.
Step 2: You are asked for the total
number of fish.
Step 3: Plug the values that you are
given into the formula and solve for
the value needed.
Multiply both sides of the equation
by 6.
6 × 7 = Total = 42 fish
Step 4: Check to be sure you used the
numbers given in the problem and
that you performed the calculations
correctly.
Here is a practice problem for you:
Lola was pleased to learn that her final grade in her history
course, which was based upon her average for 4 tests, was
90. She knew that she had scored 93, 80, and 90 on her first
three tests, but she could not remember her score on the last
test. What was Lola’s score on the fourth test?
(A) 87
(B) 90
(C) 93
(D) 97
Explanation
Step 1: You are given the score on 3 tests and the average score of 4 tests.
Step 2: The question asks for the score of the fourth test that would give the
average listed.
Step 3: Use the average formula to write the equation
with t representing the unknown score. The
denominator is 4 because the final grade of 90 was based on 4 tests even though
Lola only knew the results of 3 tests.
Solving the average equation for t, add all the numbers in the numerator.
Multiply both sides of the equation by 4 to get 360 = 263 + t. Then t is 360 − 263
which equals 97, choice (D).
Step 4: Check your math. Make sure you plugged the correct values into the
average formula in the beginning.
The ASVAB will not require you to make complex statistical calculations, but there
are a few basic statistical terms with which you should be familiar. Mean is the
same as average and is calculated the same way. The range is how “wide” the
group of numbers is and can be calculated by subtracting the smallest number
from the largest. The mode is the number that appears most frequently. Finally,
median is the middle value of a group of numbers.
Practice by identifying these terms using the number set: 1, 2, 7, −3, 0, 5, 2.
In order to apply the statistical terms to a group of numbers, the very first thing you
must do is arrange the numbers in ascending order: −3, 0, 1, 2, 2, 5, 7.
The mean of these numbers is
.
The mode of the group is 2 since it is the only number that appears twice.
The range is 7 − (−3) = 10.
The median is 2, since three numbers are smaller than that and three are larger.
Should you encounter a situation whereby there are two numbers in the middle,
the average of those two middle numbers is the median.
For instance, the median of −3, 0, 1, 2, 2, 5 is
.
SEQUENCES
A sequence is merely a group of numbers placed in order, as in the example above.
You are most likely to encounter a special type of sequence on the ASVAB called an
arithmetic sequence. The property that creates an arithmetic sequence is that
each number is equal to the number before it plus a constant number. The
sequence 1, 3, 5, 7 is an arithmetic sequence because each number is 2 more than
the previous number in the sequence. One property that makes arithmetic
sequences special is that the mean equals the median.
Here’s an example of the type of sequence problem that may be on the ASVAB:
Question
Analysis
What is the mean of a sequence of
multiples of 3 that begins with −3 and
Step 1: The question gives you the
rules of a sequence as well as the
ends with 15?
beginning and ending terms of that
sequence.
Step 2: The question asks for the
mean.
Step 3: Since the numbers are
multiples of 3, the numbers will all be
3 apart. This is an arithmetic
sequence.
You can write down the sequence: −3,
0, 3, 6, 9, 12, 15. Because this is an
arithmetic sequence, the median is
equal to the mean, 6.
Step 4: Check that you defined the
sequence properly and solved for the
correct statistical term.
PROBABILITY
Probability is the numerical likelihood that a particular outcome will occur. To find
the probability that something is going to happen, use this formula: Probability =
Probability can be expressed as a fraction, a decimal, or a percent.
Question
Analysis
If there are 12 books on a shelf and 9
of them are mysteries, what is the
Step 1: The question gives the total
number of books and the number of
probability of picking a mystery at
random?
mystery books.
Step 2: The question asks for the
probability of picking a mystery
book. In other words, it asks you for
the proportion of mystery books to
total books.
Step 3: Probability =
This probability can also be
expressed as 0.75 or 75%.
Step 4: Check that you set up and
simplified the fraction appropriately.
Probabilities are always between 0 and 1 (or between 0% and 100%). A probability
of 0 means that there are no outcomes of interest and a probability of 1 means that
all the possible outcomes result in the outcome of interest occurring.
To find the probability that both of two events will occur, find the probability that
the first event occurs and multiply this by the probability that the second event
occurs. The probability of two independent events both occurring will be less than
the probability of either occurring by itself. When you see a probability question
that deals with one event and another event both occurring, you will multiply the
probabilities.
Study the following example.
Question
Analysis
If there are 12 books on a shelf and 9
Step 1: You are given the same
of them are mysteries, what is the
probability of picking a mystery first
information about the number of
mystery books compared to the
AND a non-mystery book second if
number of books overall.
exactly two books are selected and
neither of them is replaced on the
shelf?
Step 2: This time, the question asks
for the probability that two different
events will both occur.
Question
Analysis
Step 3: The probability of picking a
mystery book first:
Probability of picking a non-mystery
book second (if a mystery is picked
first):
(Originally there were 9 mysteries
and 3 non-mysteries. A er the
mystery is selected first, there are 8
mysteries and 3 non-mysteries, i.e.,
11 books remaining.) Probability of
picking a mystery book first and then
a non-mystery book second:
Step 4: Check to be sure you set up
the second proportion to incorporate
the missing book that was already
picked. Double-check your math and
be sure you solved for the probability
that was asked for.
A question might ask you to determine the probability of one or another event
occurring. In this case, you add the individual probabilities. The probability of one
or another event occurring will be greater than the probability of either event
occurring alone.
Question
Analysis
What is the probability of rolling a 1
Step 1: The question gives you
OR a 2 on one roll of a fair six-sided
die?
background information that you are
dealing with a die that has 6 faces
and isn’t weighted.
Step 2: The question asks for the
probability of either of two scenarios
happening.
Step 3:
Probability of rolling a 1 =
Probability of rolling a 2 =
Probability of rolling a 1 or a 2 =
Step 4: Briefly check your math
before moving on to the next
question.
Practice the principles of probability on the following problem:
If a fair coin is flipped 3 times, what is the probability that
none of the occurrences will result in a head?
(A) 0
(B)
(C)
(D)
Explanation
Step 1: The question sets up a scenario of flipping coins.
Step 2: The question asks for the probability of landing on tails 3 times in a row.
Step 3: In order to flip a coin 3 times with no heads, the first flip must be a tail and
the second flip must also be a tail and the third flip must be a tail, too.
Therefore, the equation to determine the probability of no heads on 3 flips is
. Answer choice (B) is correct.
Step 4: Double-check that you solved for the correct probability and you
performed the calculations correctly.
Log in to your online resources at kaptest.com/login to watch the video
instruction on every Arithmetic Reasoning topic in this section. If you haven’t yet
registered your book, see “Welcome to Your ASVAB Studies” toward the front of
this book for registration instructions.
Arithmetic Word Problems
Learning Objectives
In this section, you will learn to:
convert word problems to equations
use common predefined formulas to answer word problems
As you may have noticed, we already started sneaking word problems into
the arithmetic review section you just completed. Word problems are
simply math problems with another step added. Generally, all you have to
do is translate the text into math and solve. In some questions, the
translation will be embedded within a “story.” Don’t be put off by the
details of the scenario—it’s the numbers that matter. Focus on the math
and translate.
TRANSLATION
O en, word problems seem tricky because it’s hard to figure out precisely
what they’re asking. The following table lists some common words and
phrases that turn up in word problems, along with their mathematical
translations.
When you see:
Think:
sum, plus, more than, added to, combined, total
+
minus, less than, difference between, decreased by
−
is, was, equals, is equivalent to, is the same as, adds up to
=
times, product, multiplied by, of
×
divided by, over, quotient, per, out of, into
÷
what, how much, how many, a number
x, n, etc.
WORD PROBLEMS WITH FORMULAS
Some of the more difficult word problems may involve translations with
mathematical formulas. The most common ones that you should know are
,
, and
, all of Word which
were discussed earlier in this chapter.
Question
Analysis
If a truck travels at 50 miles per
Step 1: The question gives you
hour for hours, how far will the
the rate of the truck and how
truck travel?
long that truck will be traveling.
Step 2: The question asks how
far the truck will go in that time.
Question
Analysis
Step 3:To answer this question,
you need to use the Time-RateDistance Formula:
.
Multiplying both sides of the
equation by time gives you:
Distance = Rate × Time
Now, plug in the numbers.
D = 50 × 6.5
D = 325 miles
Step 4:Check that you performed
the math correctly.
Try this rate problem:
Elisa rode her motorcycle for an hour and traveled
60.0 miles. Unfortunately she then encountered heavy
traffic, and it took her 2 hours to travel an additional
45.0 miles. What was her overall speed for the entire
trip?
(A) 35.0 miles/hour
(B) 45.0 miles/hour
(C) 52.5 miles/hour
(D) 60.0 miles/hour
Explanation
Step 1: The question gives you the time and distance of one portion of a
trip and then the time and distance of another portion of the same trip.
Step 2: You are asked to come up with the average speed for both portions
of the trip together.
Step 3: The total distance traveled was 60 + 45 = 105 miles.
The total time was 1 + 2 = 3 hours.
miles per hour. Answer choice
(A) is correct.
Step 4: It is important to remember that you cannot simply take the
average of the two speeds. This is because Elisa travels at each speed for a
different length of time. Make sure you use the rate formula correctly.
Log in to your online resources at kaptest.com/login to watch the video
instruction on mastering word problems. If you haven’t yet registered your
book, see “Welcome to Your ASVAB Studies” toward the front of this book
for registration instructions.
Arithmetic Reasoning Practice Set 1
Select the best answer for each question. This section has 15
questions, which is the number of Arithmetic Reasoning
questions you will see if you take the CAT-ASVAB.
1. If |y − 3| = 3, what is the greatest possible value of y?
(A)
(B)
(C)
(D)
2
4
6
8
2. Two teams are having a contest in which the prize is a box of
candy that the members of the winning team will divide evenly. If
team A wins, each player will get exactly 3 pieces of candy, and if
team B wins, each player will get exactly 5 pieces of candy. Which
of the following could be the number of pieces of candy in the
box?
(A) 325
(B) 353
(C) 425
(D) 555
3. What is the least common multiple of 7, 9, and 21?
(A)
(B)
(C)
(D)
21
63
147
189
4. What is the value of
(A) 5
(B) 7
(C) 14
(D) 35
5. A copier can make 150 copies per minute. At this rate, how many
minutes would it take to make 4,500 copies?
(A) 20
(B) 25
(C) 30
(D) 35
6. The average (arithmetic mean) age of the members in a fiveperson choir is 34. If the ages of four of the members are 47, 31,
27, and 36, what is the fi h member’s age?
(A) 29
(B) 32
(C) 34
(D) 37
7. In the past year, XYZ Corporation reported sales of $1.17 × 106. The
year before, the company’s sales were $9.00 × 105. What was the
percentage change in sales?
(A) 30% decrease
(B) 27% decrease
(C) 27% increase
(D) 30% increase
8. What is the value of 30 − 5 × 4 + (7 − 3)2 ÷ 8?
(A) 4
(B) 12
(C) 36
(D) 102
9. A group of five workers want to have a fair way of deciding who
has to perform a difficult task, so they place 4 green balls and 1
red ball into an opaque box from which each worker will draw a
ball at random. The person who draws the red ball will have to
perform the task. What is the probability that the last (5th) person
will get the red ball?
(A) 0.10
(B) 0.15
(C) 0.20
(D) 0.25
10. John's grade for a class is determined by the results of 3 tests and
1 final exam. If the exam counts twice as much as each of the
tests, what fraction of the final grade is determined by the final
exam?
(A)
(B)
(C)
(D)
11. If
, what is the value of
?
(A) 160
(B) 200
(C) 400
(D) 500
12. A full 10-liter container of diluted orange juice contains 20% water
and 80% pure juice. A er half of the diluted orange juice is
consumed, 1 liter of pure juice is added to sweeten the taste. What
is the ratio of liters of water to liters of pure juice a er the liter of
pure juice is added?
(A) 1:5
(B) 1:4
(C) 4:5
(D) 1:1
13. For all integers x, which of the following must be true about 4x +
4?
(A) Must be even
(B) Must be odd
(C) Must be a multiple of 3
(D) Must be a multiple of 5
14. A car is moving at 60 miles per hour. At this rate, how many hours
will it take for the car to travel 420 miles?
(A) 5
(B) 6
(C) 7
(D) 8
15. A building has
of its floors above ground. What is the ratio of the number of
floors below ground to the number of floors above ground?
(A) 5:2
(B) 3:2
(C) 2:3
(D) 2:5
Arithmetic Reasoning Practice Set 2
Select the best answer for each question. This section has 15
questions, which is the number of Arithmetic Reasoning
questions you will see if you take the CAT-ASVAB.
16. What is 28% of 25?
(A) 4
(B) 5
(C) 6
(D) 7
17. What is the average of
,
, and
?
(A)
(B)
(C)
(D) 1
18. How many ways are there to choose an outfit from 3 shirts and 4
pairs of pants, assuming an outfit consists of one shirt and one
pair of pants?
(A) 4
(B) 7
(C) 12
(D) 20
19. What is the value of
?
(A) 0
(B) 15
(C) 47
(D) 72
20. If
, what is the smallest possible value of
?
(A)
(B)
(C) 15
(D) 25
21. The average of x and y is 30. If z = 15, what is the average of the
three terms x, y, and z?
(A) 3
(B) 15
(C) 25
(D) 30
22. What is the value of
?
(A)
(B)
(C) 1
(D)
23. What is the greatest common factor of 50, 60, and 75?
(A) 2
(B) 5
(C) 10
(D) 25
24. A $200 watch is on sale for $160. What is the percent change in the
price of the watch?
(A) 25% decrease
(B) 20% decrease
(C) 20% increase
(D) 25% increase
25. Michael can wash a car in two hours, and Jim can wash the same
car in four hours. How long will it take the two of them working
together to wash two of the same cars?
(A) 1 hour, 20 minutes
(B) 2 hours, 40 minutes
(C) 3 hours
(D) 6 hours
26. What is the prime factorization of
?
(A)
(B)
(C)
(D)
27. In the set of numbers {1, 4, 7, 10, 13, 16, 19, 22, 25}, what is the
arithmetic mean?
(A) 13
(B) 14.5
(C) 24.5
(D) 25
28. If
, which of the following is a possible value of
?
(A)
(B)
(C) 4
(D) 24
29. For all positive values of x < 50, how many values are divisible by
both 3 and 5?
(A) 0
(B) 1
(C) 2
(D) 3
30. Three teams are having a contest in which the winning team will
split a cash prize equally among all the members of the team. If
Team 1 wins, each member will receive 10 dollars. If Team 2 wins,
each member will receive 15 dollars. If Team 3 wins, each member
will receive 25 dollars. Which of the following could be the
number of dollars in the cash prize?
(A) 120
(B) 375
(C) 750
(D) 1,250
Answers and Explanations
ARITHMETIC REASONING PRACTICE SET 1
1. C
To simplify an absolute value problem by eliminating the absolute value
function, write two equations, one of which sets whatever is inside the
vertical lines to its positive value, and the other of which sets that equal to
its negative value. So, either y − 3 = 3 or y − 3 = −3. Clearly, y has a greater
value in the first equation. By adding 3 to both sides of the equation, y = 6.
2. D
This problem tells you that the number of pieces of candy in the box can
be divided evenly by 5 and 3. So the correct answer is the choice that has
a 0 or 5 as its last digit, and the sum of whose digits is divisible by 3.
Eliminate (B) because it doesn’t end in either 0 or 5. Of the remaining
choices, only 555, (D), is also divisible by 3, since 5 + 5 + 5 = 15.
3. B
To find the least common multiple, you should identify the prime factors
of each number. The prime factor of 7 is 7, since it is a prime number. The
prime factors of 9 are 3 and 3. The prime factors of 21 are 7 and 3.
Therefore the LCM must have two factors of 3 and one factor of 7; 3 × 3 × 7
= 63. To check your work, you can confirm that 7, 9 and 21 all divide
evenly into 63.
4. B
While this problem may look formidable at first glance, it can be solved by
reducing the fraction to simpler terms before attempting to identify the
square root. When you see a complex calculation that makes you wonder
how you are going to do the math without a calculator, that is o en a hint
to use prime factorization. If you restate the problem as
you can see that many terms in the
numerator and denominator of the radical cancel out:
so that you are le with
5. C
Set up a proportion:
Now cross-multiply and solve: 150x = 4,500. So
6. A
so here the average is
Thus
;
multiply both sides by 5 to get 170 = 141 + n. Subtract 141 from both sides
and n = 29.
7. D
This is a percent change problem, so you will need to identify the original
and new values that are being compared and use the formula for
calculating percent change:
In
order to subtract powers, they must have the same base and exponent, so
you’ll have to convert one of the terms
This can be simplified to
8. B
Follow PEMDAS to get the answer. Since there is a set of Parentheses,
start there and change the expression to 30 − 5 × 4 + 42 ÷ 8. There is an
Exponent, so calculate the value of the exponent term next: 30 − 5 × 4 + 16
÷ 8. Now you can calculate the Multiplication and Division parts of the
expression from le to right to get 30 − 20 + 2. Finish up with the Addition
and Subtraction from le to right to get the answer, 12.
9. C
This is a probability question with multiple events. In order for the last
person to get stuck with the red ball, the first person must draw a green
ball and so must the 2nd, 3rd, and 4th persons. The number of green balls
will decrease with each successive pick, so the probability is
10. C
Each of the tests counts once and the final exam counts twice, which
means there are 3 + 2 = 5 total parts. The final exam is 2 parts, so it counts
as
of the final grade.
11. A
First, solve
for . Divide by 5:
so
, then divide both sides by 2 so
Square both sides,
. Lastly, multiply by 5:
.
12. A
Since half of the 10 liters of diluted juice are consumed, there must be
only 5 liters remaining. 20% is water and 80% is pure juice, so there is now
1 liter of water and 4 liters of pure juice. Another liter of pure juice is
added, so there are 5 liters of pure juice. The ratio is 1:5.
13. A
Since x is an integer, multiplying any integer by 4 will result in an even
integer. So 4x must be even. Adding 4 to an even value must result in an
even number. Therefore, 4x + 4 must be even.
14. C
The formula to use to find time when given the speed and the distance is
. Since the distance given here is 420, and the speed is
60,
15. B
The question provides a part to whole ratio and asks for a part to part
ratio. If 2 of the 5 floors are above ground, then 5 – 2 = 3 floors must be
below ground. So the ratio of floors below ground to floors above ground
is 3:2.
ARITHMETIC REASONING PRACTICE SET 2
16. D
, so multiply that by 25. However, there is a faster way to
solve this. To find the value, you would calculate
, but since
multiplication can be done in any order, this is the same as
can be simplified to
.
, and multiplying that by 28 equals 7.
17. C
The average of a set of numbers is found by adding the numbers, and
then dividing by how many terms there are. So, add the three fractions,
and then divide by 3, which is the number of terms. To add the three
fractions, start by finding the common denominator, which is 20. Then
convert each fraction to have a denominator of 20.
,
,
and
. So the sum is
. Then divide by 3 or multiply by the
reciprocal,
. The result will be
.
18. C
To find the number of possible combinations consisting of two different
elements, multiply how much of each element you have. Since each outfit
consists of one shirt and one pair of pants, take the number of shirts (3)
and the number of pairs of pants (4), and multiply them together.
.
19. C
Follow the order of operations (PEMDAS) to simplify this expression
correctly. First, simplify what is in the parentheses: in this case, 2 + 1,
which equals 3. Then apply the exponent to what's in the parentheses.
. So now the expression is
. Next, perform the
operations of multiplication and division, from le to right.
and
. The expression is now 50 – 3, which equals 47.
20. B
For an equation with an expression inside the absolute value signs, create
two equations: one with a positive value (in this case, 10) and one with a
negative value (in this case, –10). Since the question asks for the smallest
possible value of x, start with the equation with the negative value. Since
, add 5 to both sides, and the resulting equation is
.
21. C
To find the average of the three terms, first find the sum of the terms and
then divide by 3. There's no way to know the exact values of x and y, but
since the average of the two terms is 30, the sum must be 2(30) = 60. Since
z equals 15, then the sum of the three terms is 60 + 15 = 75. Lastly, divide
75 by 3, which equals 25.
22. B
First, combine the fractions in the denominator. The common
denominator of these is 10, so
and
. Once all the
denominators are the same, add or subtract the numerators: 5 + 8 – 1 =
12. So the fraction in the denominator is . Then, when dividing by a
fraction (in this case,
numerator.
), take the reciprocal and multiply that by the
. Both the numerator and denominator have a
common factor of 6, so divide both the numerator and denominator by 6,
and the fraction simplifies to .
23. B
To find common factors of a number, first break down each number into
its prime factors. Then see which factors they have in common, and find
the product of those common factors. The prime factors of 50 are 2, 5, and
5. The prime factors of 60 are 2, 2, 3, and 5. The prime factors of 75 are 3,
5, and 5. Since one factor of 5 is in each of those sets of prime factors, but
the prime factors 2 and 3 are not found in all of the numbers, the greatest
common factor is 5.
24. B
Since the price of the watch has gone down, the percent change must
represent a decrease. Using the formula for percent change, divide the
actual change by the original amount. Since the watch was originally $200
and during the sale it is $160, the watch decreased in price by $40. Divide
$40 by the original amount of $200 to get 0.2, or 20%.
25. B
Since the problem states how long it takes each person to wash the car,
the units of which are hours/car, take the reciprocal of the times to get the
rates in terms of cars/hour and add them together to get the combined
rate:
cars/hour working together. Invert that
combined rate to determine that they can wash 1 car in
hour. However,
the question asks how long it will take to wash two cars, so that would be
hours.
26. D
Don't calculate or even estimate the value of
. The prime factorization
of 26 is
. So, since there are three factors of 26, there are three
factors of 2 and three factors of 13.
, or
.
27. A
Avoid the temptation to use the formula for finding the arithmetic mean,
or average. Instead, notice that each number in the set has the same
difference from the previous number so that they form an arithmetic
sequence. Whenever that is true of a set of numbers, the arithmetic mean
is equal to the median. Since there are 9 numbers in this set, the 5th
number (when all the numbers are in order) is the median. In this case,
the 5th number is 13.
28. B
For an equation with an absolute value sign, consider both the positive
and the negative values for what is inside the signs. 4x – 6 can equal either
18 or –18. If 4x – 6 = 18, first add 6 to both sides: 4x = 24. Then divide both
sides by 4, and x = 6. However, 6 is not one of the answer choices. So try
the other equation: 4x – 6 = –18. Add –6 to both sides, so 4x = –12. Divide
both sides by 4, and x = –3.
Alternatively, the answer could be determined by backsolving. For (A),
. For (B),
.
29. D
Any number divisible by both 3 and 5 must be divisible by
, since 3
and 5 are both prime numbers. That’s 15, which is the smallest number.
Add another 15 to 15 to find the next number, 30. Then add another 15,
which equals 45. The next number would be 60, but that’s above the
range of values indicated in the question. So there are 3 possible values:
15, 30, and 45.
30. C
Since the number of dollars in the cash prize must be equally divided
among all members of each team and there is no remainder, the number
of dollars must be a multiple of each. First, find the prime factors of each
number:
,
, and
. The correct
answer will be a common multiple of the different cash prize amounts.
The least common multiple is found by taking each distinct prime factor
(in this case, 2, 3, and 5), and raising each to the highest power of each
factor. Because 2 shows up once, 3 shows up once, and 5 shows up twice,
the lowest common multiple is
. The correct answer must
have at least one 2, one 3, and two 5s to be a multiple. The factorization of
120 is
, so it's missing one factor of 5 to be a multiple.
The factorization of 375 is
, so it's missing a 2. The
factorization of 750 is
factorization of 1,250 is
, so this is a multiple. The
, so it's missing a factor of 3.
Note that because
, another way to find the
correct answer would be to look for a choice that is a multiple of 150.
, so 750 is correct.
REVIEW AND REFLECT
A er completing this chapter, think about the areas that you fully
understand. Are there any areas still giving you trouble? Pay close attention
to the themes that help you on multiple types of questions, such as finding
the least common multiple and determining factors. Also, be sure that you
practice simplifying fractions and performing basic calculations without a
calculator.
Want more instruction and practice with Arithmetic? Log in at
kaptest.com/login to watch the videos in this book's online resources and
try more questions in the Qbank.
CHAPTER 7
MATHEMATICS KNOWLEDGE
Know What to Expect
The Mathematics Knowledge subtest gives you 23 minutes to answer 15
questions, if you take the computer-adaptive test. If you take the paperand-pencil version, then you have 24 minutes to answer 25 questions.
Thus, the pace on the Mathematics Knowledge section is quicker than on
the Arithmetic Reasoning section, giving you about a minute per problem.
You may see applied arithmetic problems on the MK subtest. Review these
topics in chapter 6: Arithmetic Reasoning. Additionally, expect to see
algebra and geometry on the MK subtest.
Much of what you learned in the previous chapter about arithmetic applies
to algebra as well. The main difference between arithmetic and algebra is
that algebra involves variables as well as numbers. In this chapter, you will
learn how to work with
algebraic expressions
monomials and binomials
quadratic equations
solving for variables
inequalities
You will also learn in this chapter about geometry on the ASVAB. You will
learn the rules that apply to lines and angles and to two- and threedimensional shapes, including
triangles
quadrilaterals
circles
solid geometry
coordinate geometry
Algebra Review
The difference between algebra and arithmetic is that algebra uses
symbols called variables, such as x and y, to generalize arithmetic
relationships.
Algebra problems on the ASVAB can appear in two forms: as
straightforward math problems or as word problems. You will find that
algebra problems on the Mathematics Knowledge section are o en good
candidates for a strategic approach, such as Picking Numbers or
Backsolving. Nonetheless, if you are comfortable with algebra, using
straightforward math may be faster than using a strategy on some
problems. You want to have all these tools—Picking Numbers, Backsolving,
Strategic Guessing Using Logic, a combination of approaches, and
straightforward math—in your toolkit on Test Day.
TERMS AND EXPRESSIONS
Learning Objectives
In this section, you will learn how to:
recognize whether terms can be combined
add, subtract, multiply, and divide terms
multiply binomials and factor quadratic expressions
A term is a number, a variable, or one or more numbers multiplied by one
or more variables. Here are some examples:
4
3x
7ab2
An algebraic expression on the ASVAB test could look like this: (11 + 3x) −
(5 − 2y) If an expression consists of one term, it is a monomial. If it consists
of two terms, it is a binomial. If it consists of more than two terms, like the
one above, then it is a polynomial.
You can only add or subtract “like terms.” Like terms have the same
variables and the same exponents. The following pairs of terms are like
terms:
3a + 7a
10z2 − 5z2
To combine like terms, add or subtract the coefficients (the numbers that
come before the variables) of terms that have the same variable raised to
the same exponent as explained in chapter 6. Do not change the variables.
Here are some examples: 6a + 5a = 11a 8b2 − 2b2 = 6b2
3a + 2b − 8a = 3a − 8a + 2b = −5a + 2b or 2b − 5a Remember, you cannot
combine unlike terms such as these: 6a + 5a2
3a + 2b
Study this example:
Question
Analysis
Simplify:
(11 + 3x) − (5 − 2x)
= 11 + 3x − 5 + 2x
Distribute the minus sign across
the parentheses.
= 3x + 2x + 11 − 5
Group like terms together.
= 5x + 6
Combine like terms.
Multiplying and dividing monomials is different from adding and
subtracting them. In addition and subtraction, you can combine only like
terms. With multiplication and division, however, you can multiply and
divide terms that are different. When you multiply monomials, multiply the
coefficients of each term, add the exponents of like variables, and multiply
different variables together. Study this example:
Question
Analysis
Simplify: (6a)(4b)
= (6 × 4)(a × b)
Multiply the coefficients by each
other and the variables by each
= 24ab
other.
Now try one on your own.
Simplify: (6a)(4ab) + (3a2)(8b) = ?
Explanation
Step 1: The question presents an expression.
Step 2: You need to simplify the expression.
Step 3: Multiply the coefficients together, and multiply the variables
together. Remember not to add or subtract unless you’re dealing with like
terms.
(6a)(4ab) + (3a2)(8b) =
(6 × 4)(a × a × b) + (3 × 8) (a2 × b) =
(6 × 4)(a1+1 × b) + (3 × 8) (a2 × b) =
24a2b + 24a2b =
48a2b
The answer is 48a2b.
Step 4: Review your work to ensure you multiplied correctly.
To multiply binomials, use the FOIL method. FOIL stands for First, Outer,
Inner, Last and refers to the position of each term in the parentheses.
Here’s an example:
Question
Analysis
Question
Analysis
Simplify: (y + 1)(y + 2)
First terms: (y × y)
Use FOIL to multiply each term in
the binomials.
Outer terms: (y × 2)
Inner terms: (1 × y)
Last terms: (1 × 2)
= y2 + 2y + y+ 2
= y2 + 3y + 2
Combine like terms.
The final expression above, y2 + 3y + 2, is known as a quadratic
expression. A quadratic expression contains variables raised to the
exponent of 2, in other words, variables that are squared. An expression
without an exponent is a linear expression.
You may occasionally be called upon to factor a quadratic expression or
equation on the ASVAB. Do this with “reverse-FOIL.” Take a look:
Question
Factor: x2 − 4x − 21
Analysis
Question
(x )(x )
Analysis
To begin, build
parentheses with the
First terms that
multiply to x2.
1
−21
What Last terms will
multiply to produce
−21?
3
−7
7
−3
21
1
3
−7
Which of these pairs
will add to produce
−4?
(x + 3)(x − 7)
Plug these into the
parentheses.
Classic Quadratics
If you learn to recognize the following three common quadratics, you can
multiply them and factor them without needing to FOIL or reverse-FOIL:
Classic Quadratic
Example
(x + y)(x − y) = x2 − y2
(x + 3)(x − 3) = x2 − 9
(x + y)2 = x2 + 2xy + y2
(a + 4)2 = a2 + 8a + 16
(x − y)2 = x2 − 2xy + y2
(y − 6)2 = y2 − 12y + 36
If you see a perfect square, such as x2 or 16, on each end of a quadratic, it is
probably one of these classic quadratics.
Study this example.
Question
Which of the following is
equivalent to the expression a2 −
Analysis
Step 1: The question gives a
quadratic expression.
b2?
Step 2: You are asked to find the
answer that is the same
expression, expressed in a
different form.
Step 3: Use math knowledge to
recognize that this is a classic
quadratic.
a2 − b2 = (a + b)(a − b)
Question
Analysis
(A) (a − b)2
The answer is (C).
(B) (a + b)2
Step 4: Briefly check your
calculations.
(C) (a + b)(a − b)
(D) a2 − 2ab + b2
EQUATIONS WITH ONE VARIABLE
Learning Objective
In this section, you will learn how to:
find the value of a variable in an equation
An equation is two expressions separated by an equal sign. The key to
solving equations is to do the same thing to both sides of the equation
until you have your variable isolated on one side of the equal sign and
everything else on the other side.
Question
Analysis
Question
Solve for a:
12a + 8 = 23 − 3a
Analysis
Step 1: The question presents an
equation with one variable, a.
Step 2: The task is to find the
value of a.
Step 3: (B) is a fraction, which
makes backsolving potentially
awkward. Use straightforward
math to isolate the variable.
(A)
1
Step 4: Plug 1 in for a in the
equation:
(B)
(C)
2
(D)
11
Answer choice (A), a = 1, works
and is correct.
Try it on your own.
Solve for x: 2x + 7 =
.
Explanation
Step 1: This is a linear equation with one variable.
Step 2: You need to find the value of that variable.
Step 3: Multiply each side by 4 to eliminate the fraction: 4 × (2x + 7) =
8x + 28 = x
Subtract x from both sides:
7x + 28 = 0
Subtract 28 from both sides:
7x = −28
Divide both sides by 7:
x = −4
×4
Step 4: To confirm, plug −4 into the original equation for x:
The answer –4 works and is correct.
EQUATIONS WITH TWO VARIABLES
Learning Objectives
In this section, you will learn how to:
find the value of an expression when given the values of the
variables
solve for one variable in terms of another
find the values of two different variables when given two
equations
Sometimes a problem will give you the numerical value of the variables
and ask you for the value of an expression with those variables in it. To
solve, just plug the values into the equation. Be sure to follow the rules of
PEMDAS (see chapter 6 on arithmetic) and be careful with your
calculations.
Question
Analysis
If x = 15 and y = 10, what is the
value of 4x(x − y)?
4(15)(15 − 10)
Plug 15 in for x and 10 in for y.
= 4(15)(5)
Use PEMDAS and solve.
= (60)(5)
= 300
Sometimes you are given an equation with two variables and asked to
solve for one variable in terms of the other. This means that you must
isolate the variable for which you are solving on one side of the equation
and put everything else on the other side. In other words, when you’re
done, you’ll have x (or whatever the variable is) on one side of the equation
and an expression on the other side.
Question
Analysis
Solve 7x + 2y = 3x + 10y − 16 for x
in terms of y.
Subtract 2y from both sides to get
all the y’s on one side of the
equation.
Question
Analysis
Subtract 3x from both sides to get
all the x’s on the other side of the
equation.
x = 2y − 4
Divide both sides by 4 to isolate x.
The solution for x in terms of y is
2y − 4.
Try the next one on your own.
Solve 16t + 16u(3) + 8 = −4t − 2u − 6 for t in terms
of u.
Explanation
Step 1: You are given an equation with two variables.
Step 2: You need to solve for the variable t, but you will not end up with
one numerical value. The variable t will be equal to an expression that
contains u.
Step 3: First, use PEMDAS to simplify the le side of the equation.
16t + 18u + 8 = −4t −2u −6
Then, add 4t to both sides to get all of the t’s on one side of the equation.
20t +18u + 8 = −2u −6
Subtract 18u from both sides.
20t + 8 = −20u −6
Subtract 8 from both sides.
20t = −20u −14
Divide both sides by 20.
t = −u −
= −u −
Step 4: Check that you performed all of your calculations correctly.
SYSTEMS OF EQUATIONS
On the ASVAB, you may be presented with two equations with two
variables and be asked to solve for the value of one of the variables. There
are two ways to do this: substitution and combination.
Substitution
Using the substitution technique, you will use one equation to express one
variable in terms of the other. Then you’ll substitute that expression for
that variable into the other equation.
Question
Analysis
Question
Analysis
Find the value of x:
Step 1: The question gives you
two linear equations with two
6x + y = 15
variables.
2x − 3y = −5
Step 2: You need to solve for one
variable, x.
Step 3: It is easy to isolate y in the
first equation, so use substitution
to do so: y = −6x + 15.
Plug in −6x + 15 for y in the
second equation:
Solve for x:
Question
Analysis
Choice (C) is correct.
(A)
(B)
(C)
2
(D)
3
Step 4: Briefly confirm that you
followed PEMDAS and performed
the calculations correctly.
Alternatively, you could use Backsolving on that problem. Here’s how that
might work: answer choice (C) is probably the easiest one to start with,
since it’s a whole number. Plug 2 in for x in 6x + y = 15 and solve for y:
Then check x = 2 and y = 3 in the other equation:
The answer, x = 2, works in both equations and is correct.
Combination
The other way to solve for the value of a variable when you have two
variables and two equations is to combine the two equations by adding or
subtracting them in such a way that you eliminate one of the variables.
Then you can solve for the remaining variable.
Question
Find the value of a:
4a + 2b = 44
6a − 2b = 46
Analysis
Step 1: The question gives you
two linear equations with two
variables.
Step 2: You need to solve for one
variable, a.
Step 3: If you add the two
equations together, you will
eliminate b. This can be done by
using combination.
(A)
4
(B)
9
(C)
10
(D)
12
Choice (B) is correct.
Step 4: Briefly confirm that you
performed the calculations
correctly.
Alternatively, you could use Backsolving on that problem. Here’s how that
might work: if you decided to start with choice (B), you would plug 9 in for
a in 4a + 2b = 44 and solve for b:
Then check a = 9 and b = 4 in the other equation:
The answer, a = 9, works in both equations and is correct.
Try it on your own.
Solve for x:
Explanation
Step 1: You are given two linear equations with two variables.
Step 2: You need to find the value of one of the variables, x.
Step 3: The term 5y appears in both equations, so combination will allow
you to get rid of the y term efficiently. Rearrange the terms of the first
equation to make them easier to add together.
The correct answer is x = 4.
Step 4: To confirm your answer, check that you performed all of the
calculations correctly.
QUADRATIC EQUATIONS WITH VARIABLES
Learning Objective
In this section, you will learn how to:
solve for the value or values of a variable in a quadratic equation
When an equation has a quadratic expression on one side and zero on the
other side, you can use factoring to solve for the value or values of the
variable.
Question
Analysis
Question
Analysis
Solve for y:
y2 + 4y + 3 = 0
(y + 3)(y + 1) = 0
Factor the le side of the
equation.
If y + 3 = 0, then y = −3.
Whenever multiplication results
in zero, at least one of the factors
must equal zero. Use this fact to
solve for y.
If y + 1 = 0, then y = −1.
Therefore, y = −3 or −1.
Note that the solution to a quadratic equation o en has two values. The
only time you will get a single value for the variable is when the factors are
the same, as in this example that uses one of the classic quadratics you
learned about above:
Question
Solve for x:
x2 − 6x + 9 = 0.
Analysis
Question
Analysis
(x − 3)(x − 3) = 0
Either factor the le side of the
equation using reverse-FOIL or
use your knowledge of classic
quadratics to factor.
If x − 3 = 0, then x = 3.
Whenever multiplication results
in zero, at least one of the factors
must equal zero. Since both of
the factors are the same, you will
only get one result for x.
If you see a quadratic expression set equal to a quantity other than zero,
simply manipulate the equation so that the expression is set equal to zero.
Similarly, if you see a quadratic expression presented in a different order,
simply move the terms around in order to put it in the form ax2 + bx + c = 0.
Study this example:
Question
Solve for x:
−4 + 2x = 31 − x2
Analysis
This equation appears to have all
the parts of a quadratic equation,
but it will require some
manipulation before you can use
reverse-FOIL.
Question
Analysis
First, subtract 31 from both sides,
and add x2 to both sides, so that
the expression is set equal to
zero.
Now rearrange and combine the
terms, so that the equation has
the form ax2 + bx + c = 0.
Now you’re ready to perform
reverse-FOIL.
What are the factors of 35?
1 35
57
One of those factors will be
negative, since the third term is
negative. If so, which two
numbers listed above can have
the product of −35 and a
difference of +2?
−5 +7
Question
Analysis
Therefore, x = 5 or −7.
INEQUALITIES
Learning Objective
In this section, you will learn how to:
solve for the range of values of a variable in an inequality
PLOTTING INEQUALITIES ON THE NUMBER
LINE
An inequality is represented by one of the following four signs:
x>2
x is greater than 2.
x < −1
x is less than −1.
x−2
x is greater than or equal to 2.
x ≤ −1
x is less than or equal to −1.
Solve inequalities in the same way you have solved equations. Isolate the
variable that you are solving for on one side of the equation and put
everything else on the other side of the equation. However, when you have
solved an inequality, your solution will typically be a range of values rather
than a single value. Study the example below.
Question
Analysis
Solve for a:
4a + 6 > 2a + 10
4a − 2a + 6 > 10
Subtract 2a from both sides.
4a − 2a > 10 − 6
Subtract 6 from both sides.
2a > 4
Combine like terms.
a>2
Divide both sides by 2.
In this example, the range of possible values of a are all numbers larger
than 2. That is, a can be any value greater than 2 but cannot equal 2. Most
of the math for inequalities is the same as if you were solving an equation.
There is, however, one crucial difference between solving equations and
inequalities. When you multiply or divide an inequality by a negative
number, you must change the direction of the inequality sign. So for
example, when you divide both sides of the inequality −5a > 10 by −5 to
isolate a, you change the direction of the sign: a < −2. Because of this rule,
you cannot multiply or divide both sides of an inequality by a variable,
since you do not know whether the variable has a positive or negative
value.
To understand why this is so, consider this example, which uses integers: 1
<2
If you multiply both sides by −1:
−1 ? −2
Which is greater? The number −1 is greater than −2, so you need to use a
greater than sign: −1 > −2
The inequality sign has flipped. You can test the previous example, in
which a is less than −2, by plugging in a couple of numbers. Plug in −3 for a,
and you’ll find that (−5)(−3) > 10 becomes 15 > 10, a true statement. Plug in
a number greater than −2, say 0, and you’ll find that (−5)(0) > 10 becomes 0
> 10, which is not a true statement. Only by flipping the inequality sign do
you get the correct answer.
Try an inequality question on your own. This question does not have
answer choices. Express your answer as an inequality.
Solve for z:
Explanation
Step 1: You are given an inequality.
Step 2: You are asked to solve for the variable, z.
Step 3: First, simplify the fraction:
−2z − 3 > 4z
Isolate z on one side of the inequality by adding 2z to both sides: −3 > 6z
Divide both sides by 6:
If this were Test Day, you might see the correct answer stated that way, or it
might be reversed, like this:
Step 4: Double-check your math. Be sure to check that you used all of the
appropriate signs.
Log in to your online resources at kaptest.com/login to watch the video
instruction on every Mathematics Knowledge topic in this section. If you
haven’t yet registered your book, see “Welcome to Your ASVAB Studies”
toward the front of this book for registration instructions.
Geometry Review
Throughout the geometry problems on the ASVAB, you will be presented
with shapes and diagrams. Unless otherwise noted, you cannot assume
the drawings are drawn to scale. Thus, work using the information given in
a diagram; don’t rely on how it looks.
LINES AND ANGLES
Learning Objectives
In this section, you will learn how to:
find the length of a line segment
use the properties of straight lines, intersecting lines, and
parallel lines to solve for the value of angles
Line Segments
A line segment is a piece of a line, and it has an exact measurable length.
Questions may give you a segment divided into several pieces, give you the
measurements of some of these pieces, and ask you for the length of
another piece.
Question
Analysis
If PR = 12 and QR = 4, PQ = ?
PQ = PR − QR
Subtract QR from the whole
segment to find the remaining
piece, PQ.
PQ = 12 − 4
Plug in the lengths given and
solve.
PQ = 8
The point exactly in the middle of a line segment, halfway between the
endpoints, is called the midpoint of the line segment. To bisect means to
cut in half, so the midpoint of a line segment bisects that line segment.
M is the midpoint of AB, so AM = MB.
Angles
A right angle measures 90 degrees and is usually indicated in a diagram by
a little box. The figure above is a right angle. Lines that intersect to form
right angles are said to be perpendicular.
An acute angle measures less than 90 degrees. An obtuse angle measures
more than 90 degrees.
Angles that form a straight line add up to 180 degrees. In the figure above,
a + b = 180.
Angles around a point add up to 360 degrees. In the figure above, a + b + c +
d + e = 360.
When two lines intersect, adjacent angles are supplementary, meaning
they add up to 180 degrees. In the figure above, a + b = 180.
When lines intersect, angles across the vertex from each other are called
vertical angles and are equal to each other. Above, a = c and b = d.
Question
Analysis
Step 1: The figure shows three
intersecting lines that form six
angles, which all together equal
What is the value of x + y + z?
360°. An unlabeled angle is 90°.
Three labeled angles are x, y, and
z.
Step 2: The question asks for the
sum of the three labeled angles.
Step 3: Because the angle
labeled y is a vertical angle to the
right angle, y must equal 90°.
Because the angles labeled x and
z form a straight line with the
right angle, together they equal
180° − 90° = 90°.
y + (x + z) =
90° + 90° = 180°
Question
(A)
90
(B)
120
(C)
180
(D)
270
Analysis
Step 4: Choose option (C).
Confirm that the answer includes
the correct three angles and that
your arithmetic is correct.
Parallel Lines
Parallel lines are lines that have the same slope as one another. The slope
represents the steepness of the line and the direction it goes. Therefore,
lines that are parallel never intersect each other. You can imagine them as
being like railroad tracks. When parallel lines are crossed by another line,
this line is called a transversal, and angles are formed. All of these angles
are said to be interior angles. Angles with the same relationship to the
transversal are called corresponding angles. In the gray box below,
variables refer to the diagram above.
PROPERTIES OF ANGLES MADE BY A
TRANSVERSAL CROSSING PARALLEL LINES
Corresponding angles are equal (for example, a = e).
Alternate interior angles are equal (d = f).
Same-side interior angles are supplementary (c + f = 180).
All four acute angles are equal, as are all four obtuse angles (for
example, c = e and b = h).
Question
Analysis
Question
Analysis
Step 1: The figure shows two
parallel lines, m and n, crossed by
transversal p.
m || n
Step 2: Find the sum of the four
labeled angles.
What is the value of a + b + c + d?
Step 3: Two of the labeled angles
are acute, and two are obtuse.
Every pair of acute + obtuse
angles formed by a transversal
crossing parallel lines equals
180°.
Two acute + obtuse angle pairs =
2 × 180° = 360°.
(A)
120
(B)
180
(C)
200
(D)
360
Choice (D) is correct.
Step 4: Confirm that the answer
includes the correct four angles
and that your arithmetic is
correct.
POLYGONS
Learning Objectives
In this section, you will learn how to:
find the perimeter and area of a triangle and a quadrilateral
solve for the length of one side of a right triangle if given the
other two sides
Triangles
The three interior angles of any triangle add up to 180°. In the figure
above, x + 50 + 100 = 180, so x = 30.
An exterior angle of a triangle is equal to the sum of the two interior
angles that are not adjacent to that exterior angle. In this figure, the
exterior angle labeled y is equal to the sum of the remote angles: y = 40 + 95
= 135.
The perimeter of a polygon is the sum of the lengths of its sides. The
perimeter of a triangle is the sum of the lengths of its three sides. The
perimeter of the triangle in the figure above is 3 + 4 + 6 = 13.
The area of a triangle is equal to half of the base (that is, the length of one
leg) multiplied by the height.
Area of triangle =
(base)(height)
The height is the perpendicular distance between the side that’s chosen as
the base and the opposite vertex (opposite corner). In this triangle, 4 is the
height when the side with measure 7 (BC) is chosen as the base. In the
triangle above: Area = bh = (7)(4) = 14
Similar triangles have the same shape, but they may be different sizes.
Their corresponding angles are equal, and their corresponding sides are
proportional. The triangles shown above are similar because they have the
same angles.
Question
Analysis
Find the value of s in the diagram
above.
=
Because the triangles have the
same angle measures, their sides
are proportional. Set up a
proportion.
3s = (4)(6)
Cross-multiply to solve for s.
3s = 24
s=8
An isosceles triangle is a triangle that has two equal sides. Not only are
two sides equal, but the angles opposite the equal sides, called base
angles, are also equal.
Equilateral triangles are triangles in which all three sides are equal. Since
all the sides are equal, all three angles are also equal. All angles in an
equilateral triangle measure 60 degrees, regardless of the length of the
sides.
A right triangle is a triangle with a right angle. Every right triangle has
exactly two acute angles. The sides opposite the acute angles are called
the legs. The side opposite the right angle is called the hypotenuse. Since
it’s opposite the largest angle, the hypotenuse is the longest side of a right
triangle.
If you know two sides of a right triangle, you can solve for the third side
using the Pythagorean theorem:
a2 + b2 = c2
In this equation, a and b are the perpendicular sides, or legs, of a right
triangle, and c is the longest side, or hypotenuse, of the triangle.
Question
Analysis
One leg of a right triangle is 2 and
the other leg is 3. What is the
length of the hypotenuse?
a2 + b2 = c2
Use the Pythagorean theorem.
Plug in the lengths given for the
legs and solve for the
hypotenuse.
Quadrilaterals
A quadrilateral is a figure with four sides.
The perimeter of a quadrilateral is the sum of the measures of all four
sides. The perimeter of the quadrilateral in the figure above is 5 + 8 + 3 + 7 =
23.
A parallelogram is a quadrilateral with two sets of parallel sides. Opposite
sides are equal, as are opposite angles. The formula for the area of a
parallelogram is Area = (base)(height)
In the diagram above, the base is 2 and the height is 4, so area = 2 × 4 = 8.
A rectangle is a parallelogram containing four right angles. Opposite sides
are equal. The formula for the area of a rectangle is Area = (length)(width)
In the diagram above, the length is 7 and the width is 3, so area = 7 × 3 = 21.
As with any other polygon, the perimeter of a rectangle is all the sides
added together. Because a rectangle has two pairs of equal sides, the
formula for the perimeter of a rectangle is Perimeter = 2(ℓ + w)
The perimeter of the above rectangle is 2(7 + 3) = 2 × 10 = 20.
A rhombus has four equal sides, with the opposite sides parallel to one
another.
The formula for the perimeter of a rhombus is
Perimeter = 4s
The perimeter of the above rhombus is 4(4) = 16.
A square is a rectangle with four equal sides. Here is the formula for the
area of a square: Area = (side)2
In the diagram above, the length of each side is 6, so area = 62 = 36.
The formula for the perimeter of a square is
Perimeter = 4s
The perimeter of the above square is 4(6) = 24.
A trapezoid is a quadrilateral with one pair of parallel sides. The two
parallel sides of a trapezoid are called the bases.
The formula for the area of a trapezoid is
Area =
(sum of the lengths of the bases)(height)
In the diagram above, the area of the trapezoid is
(4 + 9)(6) = 39.
Study the example below.
Question
Analysis
The trapezoid below has an area
that is equal to greater than twice
the area of the square below.
Which of the following could be
Step 1: You’re given two shapes,
a square and a trapezoid.
Area of square = 9
the value of x?
Area of trapezoid > 2 × Area of
square
Area of trapezoid > 18
Step 2: You’re asked for the value
of x.
Question
Analysis
(A)
2
Step 3: There’s one unknown in
(B)
3
the question and numbers in the
choices, so use Backsolving.
(C)
4
(D)
5
Try choice (B): if x = 3, then
Area of trapezoid =
(4 + 5)3 =
13.5
That’s too small. Eliminate (A)
and (B).
Try choice (C): if x = 4, then
Area of trapezoid =
(4 + 5)4 =
18
That’s also too small, since the
area of the trapezoid is supposed
to be greater than 18. Eliminate
(C); (D) must be correct.
Step 4: Briefly check that your
answer makes sense and move
on to the next question.
Now try one on your own.
The value of the area of the trapezoid below is divisible
by 5 with no remainder. Which of the following is a
possible value of y?
(A)
(B)
(C)
(D)
11
12
14
18
Explanation
Step 1: The area of the trapezoid is a multiple of five. So,
(y + 11)2 = (y + 11) is a multiple of five.
Step 2: You’re asked for a possible value of y.
Step 3: Start by using Strategic Guessing Using Logic. Multiples of 5 always
end in 5 or 0. To produce a number that ends in 5 or 0, y would have to end
with 4 or 9. Only choice (C) fits.
Step 4: Briefly confirm:
(14 + 11)2 = (14 + 11) = 25, which is a multiple of
5.
CIRCLES
Learning Objective
In this section, you will learn how to:
determine the circumference and area of a circle
A circle is a figure in which each point is an equal distance from its center.
In the diagrams in this section, O is the center of the circle.
The radius of a circle is the straight-line distance from its center to any
point on the circle. All radii of a given circle have equal lengths. In the
figure above, OA is a radius of circle O.
A chord is a line segment that connects any two points on a circle.
Segments AB and AC are both chords. The longest chord that can be drawn
in a circle is a diameter of that circle.
A diameter of a circle is a chord that passes through the circle’s center. All
diameters are the same length and are equal to twice the radius. In the
figure below, AC is a diameter of circle O.
The circumference of a circle is the distance around it. It is equal to πd or
2πr. In this example, Circumference = πd = 6π
The area of a circle equals π times the square of the radius, or πr2. In this
example, since AC is the diameter, r =
= 3, and
Area = πr2 = π(32) = 9π
Study the following example.
Question
Analysis
Question
Analysis
In the figure below, the radius of
circle A has a length of 1 unit, and
the radius of circle B has a length
of 2 units. What is the ratio of the
Step 1: The question gives you
two circles and their radius
measures.
area of A to the area of B?
Step 2: You need the ratio of the
area of A to the area of B. The
answer choices are all expressed
as fractions, so it will look like
this:
Step 3: Calculate the area of
each.
Area of A = π12 = π
Area of B = π22 = 4π
Question
Analysis
Step 4: Choice (A) is correct.
Briefly double-check your
calculations and confirm.
(A)
(B)
(C)
(D)
Now, try this one on your own.
The diameter of the circle below has measure x. The
area of the circle is 64π. What is the value of x?
(A)
(B)
(C)
(D)
4
2π
8
16
Explanation
Step 1: The question supplies this information:
A = 64π
d=x
Step 2: You’re asked for the measure of the diameter, or x.
Step 3: Work backwards from what you know.
A = 64π = r2π
r2 = 64
r=8
x = diameter = 2r = 16
Step 4: Choice (D) is correct. Briefly double-check your math and confirm.
SOLID GEOMETRY
Learning Objective
In this section, you will learn how to:
find the volume and surface area of a rectangular solid
These formulas pertain to a rectangular solid box. Length is ℓ, width is w,
and height is h.
Volume of a rectangular solid or box = ℓ × w × h Surface area of a
rectangular solid or box = 2ℓw + 2wh + 2ℓh
Question
Analysis
Find the volume of the box in the
figure above.
V=ℓ×w×h
Use the formula for the volume of
a rectangular solid.
V = 8 × 5 × 6 = 240
Plug in the dimensions given and
solve.
Now try a problem on your own.
Find the surface area of the box above.
Explanation
Step 1: The question provides a diagram of a box.
Step 2: The question asks for the surface area of that box.
Step 3: Use the formula for surface area of a rectangular solid, plug in the
values given, and solve: SA = 2ℓw + 2wh + 2ℓh
SA = (2 × 8 × 5) + (2 × 5 × 6) + (2 × 8 × 6)
SA = 80 + 60 + 96 = 236
Step 4: Confirm that you plugged in the correct values for the correct
variables.
To find the volume of a cylinder, you find the area of its base (which is a
circle) and multiply it by the height.
Volume of a cylinder = πr2h
Question
Analysis
Find the volume of the cylinder in
the figure above.
V = πr2h
Use the formula for the volume of
a cylinder.
Question
V = π × 22 × 5 = π × 4 × 5 = 20π
Analysis
Plug in the dimensions given and
solve.
To find the surface area of any three-dimensional figure, add the areas of
each side of the figure. Accordingly, finding the surface area of a cylinder
involves adding the area of both of the circular ends to the area of the
curved sides. Note that, if the sides of a cylinder were “unrolled,” they’d
form a rectangle like this:
Thus, the formula for the surface area of a cylinder is:
SA = 2(πr2) + 2πrh
COMBINED FIGURES
When you are presented with a diagram that looks like two shapes put
together, consider splitting the shapes to make calculations easier. For
example, take a look at the next question:
Question
Find the area of the figure above.
Analysis
Note that the figure is half of a
circle sitting on top of a
rectangle. Split the figure up and
work with the two shapes
independently.
Area = ℓ × w = 7 × 4 = 28
Plug the values from the diagram
into the area formula for a
rectangle.
Area = πr2 = π(2)2 = 4π
Since 4 is the diameter of the
circle, 2 is the radius. Use that
information in the area formula
for a circle.
4π ÷ 2 = 2π
Since it is only half of a circle, you
need to divide the area by two.
28 + 2π
Add the area for the rectangle
and the area of the half circle
together to get your answer.
If you see a complicated figure on the test, try to break it down into more
manageable components and solve for each individually.
COORDINATE GEOMETRY
Learning Objectives
In this section, you will learn how to:
choose the equation that correctly represents a given line
calculate the slope and y-intercept of a line if given two points on
the line
find the distance between two given points on a coordinate
plane
The coordinate grid is composed of a horizontal x-axis and a vertical yaxis. The place where the axes meet is called the origin. Every point on the
coordinate grid has a pair of coordinates, with the first being the xcoordinate and the second being the y-coordinate. In the figure above,
points A, B, and C are at (3, 2), (–2, 3), and (–3, –5), respectively.
A line on the coordinate grid can be represented by the slope-intercept
form of a linear equation. In this equation, x and y are the coordinates of a
point on the line, b is the y-intercept, and m is the slope. Study the
examples below.
Slope-intercept form of a linear equation: y = mx + b
The y-intercept is the point where the line crosses the y-axis. The xcoordinate is always zero at the y-intercept.
The slope defines if a line goes down to the right or up to the right. Slope
can be thought of as “rise over run” or “change in y over change in x.”
Slope =
If a line has a positive slope, then y gets larger as x gets larger. If a line has a
negative slope, then y gets smaller as x gets larger. The steeper the line, the
greater the absolute value of the slope. For example, lines with slopes of –3
or 3 are steeper than lines with slopes of –1 or 1, which in turn are steeper
than lines with slopes of
or
.
Study this example about the coordinate plane.
Question
Analysis
A line on the coordinate grid has
a slope of 2 and a y-intercept of
−8. What is the correct equation
of this line?
y = mx + b
Use the slope-intercept equation
for a line.
y = 2x − 8
Plug in 2 for m and −8 for b.
Now try this coordinate geometry problem on your own.
The following points lie on a line on the coordinate grid: (0, 2) and
(6, 5). What is the slope of this line?
Explanation
Step 1: You are given two points on a coordinate grid.
Step 2: You need to find the slope of the line that contains these two
points.
Step 3: Use the formula for the slope of a line:
Slope =
Plug in the y-coordinates from the second point and the first point,
respectively, and the x-coordinates in the same order.
Slope =
=
=
Step 4: Check your math and your fraction reduction. The line has a slope
of
.
If you know the slope of a line and one point on that line, you can calculate
the y-intercept. Continuing the example above, plug the information into
the slope-intercept formula and solve for the y-intercept.
Question
Analysis
Find the y-intercept of the line
that includes points (0, 2) and (6,
5).
y = mx + b
Use the slope-intercept formula.
y=
Plug in the slope, which was
x+b
calculated above to be
, for m
in the equation.
2=
x×0+b
Plug in the x- and y-values from
one pair of coordinates.
Question
2=0+b
Analysis
Solve for the variable b.
2=b
If you are given two points on a grid and asked to find the distance
between them, you can do so using the Pythagorean theorem. Continuing
to use the points above, find the distance between the two points on the xaxis and the difference between the two points on the y-axis. Then, using
those two values as the legs of the right triangle, calculate the hypotenuse,
which is the distance between the points.
Question
What is the distance between the
two points (0, 2) and (6, 5)?
Analysis
Question
Analysis
Draw the points on a coordinate
plane. Then, draw a third dot that
makes a right triangle when all
points are connected. The third
point will be drawn where the yaxis of one point crosses the xaxis of the other.
The distance along the x-axis is 6
and the distance along the y-axis
is 3.
Use the Pythagorean theorem to
solve for the distance between
the two points.
The distance between the two
points is
.
Note: The triangle also could
have been drawn with the third
point opposite, with the y-axis of
the lower point intersecting the
x-axis of the higher point. Either
way, the result is the same.
If you are asked to find the distance between two points on the coordinate
plane, draw a right triangle to help you use the Pythagorean theorem to
solve.
Log in to your online resources at kaptest.com/login to watch the video
instruction on every topic in this section. If you haven’t yet registered your
book, see “Welcome to Your ASVAB Studies” toward the front of this book
for registration instructions.
Mathematics Knowledge Practice Set
1
Select the best answer for each question. This practice set contains
15 practice questions, which is the number of Mathematics
Knowledge questions you will see if you take the CAT-ASVAB.
1. What is the height of a rectangular box with volume of 140, length
of 10, and width of 7?
(A)
(B)
(C)
(D)
2. If x =
2
17
70
9,800
, y = 2, and z =
, then x2 − 5yz + y2 =
(A)
(B)
(C)
(D)
1
2
4
7
3. Solve for a:
(A) a < –240
(B) a > 240
(C) a > 180
(D) a > 40
4. (3d − 7) − (5 − 2d) =
(A) d − 12
(B) 5d − 2
(C) 5d + 12
(D) 5d − 12
5. Which of the following are possible values of x, if x2 − x − 20 = 0?
(A) −5, 4
(B) −4, 5
(C) −2, 10
(D) 5, 4
6. The following two points lie on a line on the coordinate grid: (−2, 0)
and (4, 6). Which of the following is the equation of the line?
(A) x = y + 2
(B) y = 3x + 6
(C) y = 2x + 1
(D) y = x + 2
7.
If the perimeter of the above square is 36, what is the
circumference of the circle?
(A) 6π
(B) 9π
(C) 12π
(D) 18π
8.
What is the area of the frame in the above diagram if the picture
inside has a length of 8 and a width of 4?
(A) 16
(B) 24
(C) 48
(D) 56
9.
In the figure above, what is the distance from the midpoint of
to the midpoint of
?
(A) 12
(B) 14
(C) 16
(D) 18
10. If s − t = 5, what is the value of 3s − 3t + 3?
(A) 11
(B) 12
(C) 15
(D) 18
11. Given the equation
, if y = 3, what is the value of x?
(A)
(B) 1
(C) 2
(D) 4
12. At what point do the lines described by the equations y = 3x – 8 and
y = –x + 4 intersect?
(A) (–1, –3)
(B) (–3, –1)
(C) (1, 3)
(D) (3, 1)
13. Given the equation
, what is r in terms of w and k?
(A)
(B)
(C)
(D)
14. If b < 0 and
, which of the following is always true?
(A)
(B)
(C) ad > bc
(D) a < bcd
15.
In the parallelogram above, if x = 4y, what is the value of z?
(A) 36°
(B) 108°
(C) 135°
(D) 144°
Mathematics Knowledge Practice Set
2
Select the best answer for each question. This practice set contains
15 practice questions, which is the number of Mathematics
Knowledge questions you will see if you take the CAT-ASVAB.
16. Which of the following statements cannot be true under any
circumstances?
(A) Triangle ABC is an equilateral right triangle.
(B) Triangle ABC is an isosceles right triangle.
(C) Triangle ABC has three acute interior angles.
(D) Triangle ABC has an interior angle greater than 170°.
17.
In the figure above, what is the area of the semicircle that is on top
of the square if the area of the square is 400 cm2?
(A)
(B)
(C)
(D)
18. If 7x + 2y = x – 4y and both sides of the equation equal 15, what is
the value of x?
(A) –3
(B) 1
(C) 3
(D) 6
19.
If the area of the triangle above is 6, what is the perimeter?
(A) 9
(B) 12
(C) 15
(D) 18
20. If the perimeter of an equilateral triangle is 24 cm, what is its area?
(A)
(B)
(C) 24
(D)
21. Solve
(A) 2
(B) 5
(C) 10
(D) 20
for x.
22.
If the straight line in the graph were extended to a point where y =
100, what would be the value of x at that point?
(A) 100
(B) 102
(C) 200
(D) 202
23. The Greek letter delta, Δ, represents the sensitivity of the price of
stock options to price movements of the stock upon which the
derivative option is based. If an option has Δ = 0.50, then a $1.00
increase in the underlying stock should result in a $0.50 increase in
the value of that option. Joseph owns an option on 200 shares of
XYZ Corporation. That stock is currently priced at $45.00 per share.
If the price of the stock of XYZ were to decrease by 2%, what would
be the expected change in the value of Joseph's option if its Δ =
0.40?
(A) –$72
(B) –$36
(C) $36
(D) $72
24.
In the figure above, ED = 3 cm, CD = 5 cm, and BA = 4 cm. What is the
perimeter of triangle ABC?
(A) 12 cm
(B) 15 cm
(C) 16 cm
(D) 18 cm
25. A teacher accompanied her students on a trip to the museum. She
wanted to be certain that she kept track of all the students during
the trip, so she counted the students by the color of the coats they
were wearing. One-half of the students wore black coats, one-sixth
wore red, one-fourth wore blue, and the remaining two students
wore green. How many students went on the trip?
(A) 12
(B) 24
(C) 36
(D) 48
26. Which of the following equations describes a straight line on a
standard coordinate plane?
(A) x = 3
(B)
(C) z = 2x + y
(D) y = x2 + 3
27.
Quadrilateral ABCD is a parallelogram. Vertex A is located at (–5, –2),
vertex B has coordinates (–3, 3), and the position of vertex D is (5, –
2). What is the length of diagonal AC?
(A) 10
(B) 13
(C) 15
(D) 20
28. If x + y = 2 and x2 – xy – 10 – 2y2 = 0, what does x – 2y equal?
(A) 0
(B) 1
(C) 2
(D) 5
29. If each side of a regular hexagon is 6 cm long, what is the area of the
hexagon?
(A)
(B)
(C)
(D)
30. If a is an integer and 2a2 + a = 28, what is the value of a?
(A) –4
(B) 0
(C) 4
(D) 7
Answers and Explanations
MATHEMATICS KNOWLEDGE PRACTICE SET 1
1. A
This question involves a rectangular box, so you are working with a
geometric solid. You are given the box’s volume and two of its
dimensions, and you’re asked for the third dimension. The volume of a
rectangular solid is found by multiplying the figure’s three dimensions, ℓ
× w × h. Each of those dimensions has to be smaller than the volume.
Therefore, you can rule out (D) right away—it’s way too big.
Now you can choose to backsolve or use straightforward math. If you
backsolve, start with (B) 17, and see what happens: 10 × 17 is already
170, which is greater than 140. So 17 is too big, and the answer must be
(A). To confirm, check whether 10 × 7 × 2 equals 140. It does, and (A) is
the correct answer.
The straightforward math looks like this:
2. B
You’re given values for three variables and asked to solve an equation
with those three variables. Plug the values into the equation and solve
with arithmetic: x2 − 5yz + y2 = (
)2 − 5(2)
+ 22 = 3 − 5 + 4 = 2.
3. B
This question gives you an inequality and asks you to solve for a
variable, a. First, get the only term with an a in it by itself on one side of
the inequality by subtracting 20 from both sides:
< −120. Now
multiply each side by –2, remembering to switch the inequality sign
because you are multiplying by a negative number: a > 240.
4. D
This question involves an equation with one variable, and the answer
choices are simplified forms of the equation. You can use Picking
Numbers or straightforward math to solve.
Try picking 2 for d. Then (3d − 7) − (5 − 2d) = (3 × 2 − 7) − (5 − 2 × 2). Use
PEMDAS to solve: (6 − 7) − (5 − 4) = –1 − (1) = –2. −2 is your target number.
Now plug 2 in for d in each of the answer choices to see which gives you
the target number −2: (A) 2 − 12 = −10; (B) 5(2) − 2 = 8; (C) 5(2) + 12 = 22;
(D) 5(2) − 12 = −2. (D) is the correct answer.
If you use algebra to solve, start by eliminating the parentheses by
distributing the minus sign over the second set of parentheses: (3d − 7) −
(5 − 2d) = 3d − 7 − 5 − (−2d) = 3d − 7 − 5 + 2d. Now combine like terms and
perform the addition and subtraction: 3d + 2d − 7 − 5 = 5d − 12.
5. B
A quadratic expression is set equal to zero and you are asked to find a
pair of values that x could equal. Factor the equation by finding a pair of
numbers that multiply to −20 and add to –1. Those numbers are −5 and
4, so the equation becomes (x + 4)(x − 5) = 0. When multiplication results
in zero, at least one factor must be zero. If x + 4 = 0, then x = −4; if x − 5 =
0, then x = 5.
You could also use Backsolving here. Because 4 appears in two answer
choices, try it first: 42 − 4 − 20 = −8 ≠ 0. So x cannot be 4, and you can
eliminate (A) and (D). Now try 5: 52 − 5 − 20 = 0. That works! Of the two
remaining choices, only (B) has 5 as a value of x, so that is the correct
answer.
6. D
The question gives two points on a line and asks for the equation of the
line. Three of the equations in the answer choices are in slope-intercept
form: y = mx + b. Choice (A) starts with x, which you might recognize as
not being the correct form of an equation of a line. Therefore, in order to
evaluate (A), you should convert it to the format y = x − 2.
Slope is
. The coefficient
of x is 1.
Find the y-intercept by plugging one of the coordinate pairs and the
slope into the y = mx + b equation: 6 = (1)(4) + b; b = 2.
Plug 1 in for m and 2 in for b in the slope-intercept equation to get the
answer. y = 1x + 2, which can also be written y = x + 2. Choice (D) is the
correct answer.
7. B
This question shows a circle inscribed inside a square. It says that the
square’s perimeter is 36 and asks for the circle’s circumference. A square
has four equal sides, and the formula for the circumference of a circle
requires knowing either the radius or the diameter of the circle. Your
task is to take the information you’re given about the square and apply
it to the circle.
If the perimeter of the square is 36, then each of the four sides equals
= 9. The side of the square is the same length as the diameter of the
circle, so the diameter of the circle is also 9. Finally, the circumference is
πd = 9π.
If it’s more efficient for you, you can backsolve this question. Start with
(B). If the circle’s circumference is 9π , then its diameter is 9. That makes
the side of the square also 9, and the square’s perimeter is 4 × 9 = 36.
That matches the information in the question, and you know that (B) is
correct.
8. C
The diagram shows one rectangle inside another and the dimensions of
the larger rectangle. The question says this is a picture in a frame and
gives the dimensions of the smaller rectangle (the picture). You need to
find the area of the frame. The area of the frame is the area of the larger
rectangle minus the area of the smaller rectangle, (8 × 10) − (4 × 8) = 80 −
32 = 48.
9. A
The diagram gives a number line with four points labeled. The question
names two line segments and asks for the distance between their
midpoints. First, find the midpoints and then calculate the distance
between them. To find the midpoint of a segment on the number line,
add the endpoints and divide the sum by 2. The midpoint of PQ is
. The midpoint of RS is
. Finally, the distance between the two points
is the positive difference between their coordinates, 5 − (−7) = 12.
10. D
You’re given an equation with two variables and asked for the value of
an expression with the same two variables. You might notice that the
variables in the second expression contain the variables in the first
expression multiplied by 3. If s − t = 5, then if you multiply both sides by
3, you get 3s − 3t = 15. Thus, 3s − 3t + 3 = 15 + 3 = 18.
Alternatively, you could pick numbers for s and t so that s − t = 5; say s =
7 and t = 2. Now plug those values into the expression and solve: 3s − 3t
+ 3 = 21 − 6 + 3 = 18.
11. C
This problem has an equation with two variables, but it provides the
value of one of the variables. It could be solved by simplifying the
equation to get x in terms of y, but plugging in 3 for y in the equation is a
more straightforward way to get the answer.
12. D
The question gives the equations for two straight lines in standard y =
mx + b form and asks at what point the lines intersect. While it may be
tempting to draw the lines, this question can be answered using algebra.
At the point where the two lines intersect, both their x and y values will
be equal. The question provides two different equations for y, so start by
setting these equal to each other: 3x – 8 = –x + 4. Add x to both sides: 4x –
8 = 4. Add 8 to both sides: 4x = 12, so x = 3. Therefore, the x value at the
point where the lines intersect is 3. To find the y value for this single
point, plug 3 in for x in either equation: 3(3) – 8 = 1 or –(3) + 4 = 1. The
proper listing for an ordered pair of coordinates is (x, y), so (3, 1) is
correct.
13. B
The question contains an equation with three variables and asks you to
solve for one of the variables in terms of the other. Starting with
,
Multiply both sides by k + w:
Subtract 3k from both sides:
Combine like terms:
Divide both sides by w:
14. A
The question gives an inequality with four variables, one of which must
be a negative number, and asks which of the inequalities in the answer
choices must be true. If both sides of the original inequality are
multiplied by b, the resulting inequality will have a on one side and
on the other. The question stem states that b is negative. When
multiplying or dividing an inequality by a negative number, the
inequality sign must be "flipped." Therefore, (A) rather than (B) is
correct. Choice (C) could be true if d were positive, but the question
does not limit d to positive numbers. Choice (D) is mathematically
incorrect; the inequality cannot be algebraically manipulated to
establish a relationship between a and the product of b, c, and d.
15. D
The question consists of a parallelogram with certain angles given as
variables and asks you to use that information to calculate a numerical
value for one of the variables. Since opposite angles in parallelograms
are equal, the measurement of z will be the same as x. Adjacent angles
in parallelograms add up to 180°, so x + y = 180°. Substituting 4y for x, 4y
+ y = 5y = 180°, so y = 36° and x = z = 180° – 36° = 144°.
MATHEMATICS KNOWLEDGE PRACTICE SET 2
16. A
The question asks which of the answer choices is never true (is always
false). A glance at the choices reveals that the question deals with
properties of triangles. An equilateral triangle has three 60° interior
angles. A right triangle must have one interior angle of 90°. Therefore,
there is no such thing as a "right equilateral triangle." An isosceles
triangle could have angles of 45°, 45°, and 90°, so (B) could be a true
statement. Since the total of the interior angles of a triangle is 180° and
acute angles are less than 90°, there are unlimited combinations of three
acute interior angles, so (C) could be true. An equilateral triangle, with
each of the three angles equal to 60° is a prominent example. Similarly,
a triangle could have one obtuse angle between 170° and 180°, although
the other two angles would be very small. For example, a triangle could
have interior angles of 172°, 5°, and 3°, so (D) could be a true statement
as well.
17. C
The question states that the two parts of the figure are a semicircle and
a square, so you can use the properties of those geometric figures to
answer the question. The side of the square is the same as the diameter
of the semicircle. The area of a square is the length of a side squared, so
s2 = 400 cm2 and s = 20 cm. The area of a circle is
, so the area of a
semicircle is
. Since the side of this square is 20 cm, the diameter of
the circle is also 20 cm. The radius is half that, or 10 cm. Plug that value
into the formula for the area of a semicircle:
.
18. C
The question has one equation with two variables, and both sides of the
equation have the same value. You are asked to solve for one of the
variables. Merely knowing x + 2y = x – 4y will not be enough to solve the
problem, since we can't solve one equation with two variables. Instead,
set up two different equations: 7x + 2y = 15 and x – 4y = 15. Multiply the
first equation by 2 so that the y coefficient becomes 4:
2(7x + 2y) = 2(15)
14x + 4y = 30
Add this to the second equation:
+(x – 4y = 15)
And the y coefficient becomes 0:
15x = 45
So x = 3. Since this is all that the question asked, there is no need to
solve for y.
19. B
The question provides a value for one leg of a right triangle and the area
of that triangle and asks you to calculate the perimeter. The area of a
triangle can be calculated using the formula
. Since this is a
right triangle, the two legs are the base and height, so
and
b = 4. Use the Pythagorean theorem to find the hypotenuse: 32 + 42 = h2.
(This is a "pattern" 3:4:5 right triangle; using that fact is quicker than
using the Pythagorean theorem.) The perimeter is 3 + 4 + 5 = 12.
20. D
The question states the perimeter of an equilateral triangle and asks you
to determine the area. Drawing a quick sketch can help to answer this
question.
Since the three sides are equal, the length of a side is
. The dotted line is the height of the triangle. Since the height
bisects the base at a right angle (as the sketch shows), it creates right
triangles with one leg of 4 cm and a hypotenuse that is 8 cm. The height
can be calculated using the Pythagorean theorem:
, so
;
. The area of a triangle is
, and
.
21. C
The question has a complex single variable equation with "stacked"
fractions and asks you to solve for the value of the variable. In order to
isolate the variable x, you will first need to simplify the equation using
PEMDAS.
Parentheses
Exponents
Multiplication
Now continue to solve by multiplying both sides of the equation by the
denominator of the le side:
Multiply both sides by x: 12x = 10x + 20. So 2x = 20 and x = 10.
22. D
The graph shows a portion of a straight line and asks what would be the
value of the x-coordinate if the line were extended so that y = 100. In
order to answer this question, you will first need to determine the
equation for the line shown on the graph in the standard y = mx + b form.
Two good reference points that the line passes through are (2, 0) and (0,
–1). The slope, m, is
. Since b is the y-intercept, the second
point (or the graph itself) shows that b = –1. So the line is defined by the
equation
. Substitute 100 for y:
. Multiply
both sides by 2: 200 = x – 2, so x = 202.
23. A
This is a word problem that requires careful attention to the details of
the application of an unfamiliar variable with percentage changes. The
question asks for the dollar change of Joseph's option based upon a
percentage change in the underlying stock. Start by converting the price
change of the stock to dollars. Since the change was a decrease, (–2%)
($45) = –$0.90. Applying the Δ of 0.40 to this change, option values
would decrease by (0.40)($0.90) = $0.36 per share. However, Joseph's
option is based on 200 shares of the stock, so his expected change in
value would be
.
24. C
The question diagram shows two triangles with a common vertex and
states that two of the line segments that are sides of the triangles are
parallel. Since angle BAC is a right angle and ED and BA are parallel,
angle CED must also be a right angle. Additionally, angles BCA and ECD
are vertical angles, so they must be equal. Consequently, the two
triangles are similar. The question asks you to determine the perimeter
of ΔABC. Given that the two triangles are similar and the ratio BA:ED =
4:3, the length of each side of ΔABC will be the corresponding side of
ΔCED. The legs of ΔCED are 3 cm and 4 cm, so the hypotenuse must be 5
cm (32 + 42 = 52) and the perimeter is 3 cm + 4 cm + 5 cm = 12 cm. The
perimeter of ΔABC is
25. B
The problem subdivides a group by a combination of fractions and a
whole number and asks you to determine the number of members of
the group. The makeup of the group can be expressed as
, where T represents the total number of
students. Convert the fractions to their least common denominator (12)
so that they can be added:
. Thus,
, so T = 24.
Instead of setting up an equation, you could have chosen to backsolve.
Start by trying out (C), for instance. If there were 36 students, 18 (onehalf) would have worn black coats, 6 (one-sixth) red coats, and 9 (onefourth) blue coats. Since 18 + 6 + 9 = 33, that would mean that 36 – 33 = 3
students wore green, so 36 is too many. Try (B): 12 + 4 + 6 = 22. Since
there are 24 – 22 = 2 students le over wearing green coats, (B) is correct.
26. A
The question asks you to determine which of the answer choices can be
plotted as a straight line on the coordinate plane. Since x = 3 does not
include y in the equation, you might be tempted to eliminate this
answer. However, because y does not appear in the equation, x = 3 for all
values of y. Thus, this equation represents a straight, vertical line
crossing the x-axis at 3. You can verify that
is not a straight line
by picking 3 numbers for x such as 1, 2, and 3. The corresponding y
values are 1, , and . Since y decreases by different amounts for the
same increase in x, this is not a straight line. Eliminate choice (B). Choice
(C) can be eliminated because it contains three variables; the coordinate
plane has only two. (This equation might describe a straight line in three
dimensions.) Choice (D) has the term x2, so it is not a linear equation and
therefore would not be graphed with a straight line.
27. B
The question lists the coordinates of three of the four corners of a
parallelogram and asks you to find the length of the diagonal that ends
at the corner with unknown coordinates. First, determine the
coordinates of vertex C. Because the figure is a parallelogram, line
segments AB and CD will be parallel and of equal length. The xcoordinate of B (–3) is 2 greater than the x-coordinate of A (–5), so the xcoordinate of C will be 2 greater than that of D, or 7. Similarly, the ycoordinate of B is 5 greater than that of A, so the coordinates of C are (7,
3). To find the length of a "slanted" line in coordinate geometry,
construct a right triangle with the line of unknown length as the
hypotenuse, as shown in the diagram below, by dropping a
perpendicular vertical line from C to the extension of AD to create new
point E:
AC is the hypotenuse of right triangle AEC. Leg AE is 12 units long (7 –(–
5)), and leg CE is 5 units long (3–(–2)). Applying the Pythagorean
theorem, AC2 = 122 + 52 = 144 + 25 = 169.
.
28. D
The question provides two equations with two variables and asks for the
value of an expression containing both variables. Ideally, you can solve
directly for the value of x – 2y rather than having to solve for each
variable individually. Since one of the equations is a quadratic, make it
easier to factor by adding 10 to each side of x2 – xy – 10 – 2y2 = 0. Thus x2
– xy – 2y2 = 10. The x2 terms can result from the multiplication of two
factors, so
. The missing terms will have a product
of –2y2, so they will be either –2y and y or –y and 2y. Since their sum
must have a coefficient of –1 (the same numerical coefficient as in the
middle term of the quadratic), then the individual terms must be y and –
2y, so (x + y)(x – 2y) = 10. The question tells you that x + y = 2, so
substitute that value to get 2(x – 2y) = 10, and then x – 2y = 5.
29. B
The question describes a regular hexagon with sides 6 cm long and asks
you to determine the area of the hexagon. Like many complex geometry
questions, this one can be solved by subdividing the figure into smaller,
less complex shapes.
A hexagon can be divided into 6 triangles with a common vertex at the
center as shown above. Since a regular hexagon is symmetrical, all 6 of
the triangles will be identical (congruent). Therefore, the area of the
entire hexagon will be 6 times the area of one of the triangles. There are
6 triangles that share the common vertex C, so each of the angles at that
point will be
. Since C is at the center of the hexagon, it is
equidistant from each vertex, so AC = BC and, therefore,
Because all three angles total to 180° and
,
. Thus,
is an equilateral triangle.
.
In order to calculate the area of ABC, draw an altitude from C to X. This
dotted line bisects and is perpendicular to AB. If each side of the
hexagon is 6 cm, then AX = 3 cm and, because ABC is equilateral, AC = 6
cm. Use the Pythagorean theorem to determine the length of CX:
, so
. The area of a triangle is
, in
this case
. This is the area of AXC; the area of
ABC is twice that amount or
, and the total area of the hexagon is
.
30. A
The question contains a quadratic equation with one variable and also
tells you that the variable is an integer. You are asked to find a single
solution for the variable's value. Start by rearranging the equation into
the standard quadratic form, 2a2 + a – 28 = 0. When factored, that will be
. The factors of the coefficient of the first term (2) are 2
and 1. The factors of the third term (–28) could be 1 and –28, –1 and 28, 2
and –14, –2 and 14, 4 and –7, or –4 and 7. You need to find a combination
of the two sets of factors and signs that will produce a sum of 1, which is
the coefficient of a in the second term of the quadratic equation. The
correct combination would be
and
, since
and
. The factored equation is (2a – 7)
(a + 4) = 0. If 2a – 7 = 0, then a = 3.5, but that is not an integer. If a + 4 = 0,
then a = –4, which is a negative integer. Note that it was not necessary to
include the negative factors of the first term –a and –2a since that would
have produced factors of (–2a + 7) and (–a – 4), which have the same two
solutions, 3.5 and –4.
Alternatively, backsolve to answer this question. Substitute –4 for a to
see if the result is 28:
. It is not
necessary to check the other choices.
REVIEW AND REFLECT
A er this chapter and these practice question sets, how comfortable do
you feel with algebra? Which concepts do you need to review? How o en
were you able to spot the opportunity to use a strategy like Backsolving or
Picking Numbers?
Also, how did you do on the items related to geometry—which formulas do
you know, and which do you need to brush up on?
Use your thoughts about these questions to guide your review of this
chapter.
CHAPTER 8
CONQUERING THE TECHNICAL
SUBTESTS
Congratulations! If you’ve been working through this book in order, then
you’ve reviewed all of the portions of the AFQT, which is crucial for your
eligibility to enlist in the armed forces. However, perhaps you don’t just
want to enlist—you may want to enlist and to qualify for a specific job.
There are many varieties of specialized job opportunities in the armed
forces, which could form the foundation for a lifelong military career or
could prepare you for a successful career in civilian life a er you’ve
completed your military service. Doing well on the ASVAB’s technical
subtests, in addition to the AFQT, is important for qualifying for many of
those specialized jobs.
The next six chapters will prepare you for the ASVAB technical subtests:
General Science, Electronics Information, Auto Information, Shop
Information, Mechanical Comprehension, and Assembling Objects. The
amount of emphasis you should give to each of these chapters will depend
on which job or jobs you desire. Be sure to speak with a recruiter, do your
research, and form a sense of which subtests are most important for your
goals. That knowledge, combined with your performance on the Diagnostic
Test which forms chapter 2 of this book, will tell you which topics you need
to study most.
If you aren’t sure which career path you are interested in, pay attention to
your strengths and the parts of the ASVAB you enjoy. If there is a particular
topic that is of interest to you and you would like to learn more about it,
you can use that passion to help you decide a potential career path.
Conducting online research and speaking to a recruiter can help you
determine which paths would help you pursue your interests in the best
way. This information can help focus your study time on the most
beneficial sections of the test for your ideal path.
THE KAPLAN METHOD FOR THE
ASVAB TECHNICAL SUBTESTS
Learning Objective
In this section, you will learn to:
apply the Kaplan Method for the Technical Subtests to ASVAB
questions
STEP 1: IDENTIFY WHAT YOU ARE BEING ASKED FOR.
Just as with math questions, it’s very important to figure out what your
task is. Does the right answer represent the value of a variable? The name
of a planet? The definition of a unit of measure? The name of a type of
tool? How much force is required to move an object? and so on.
O en, a quick glance at the answer choices can help point you in the right
direction. Don’t read them in depth at this point—save that for Step 4.
Simply use them to get a sense of what your task is. If all the answer
choices are numbers followed by “mHz,” you will be calculating the
frequency of a wave and expressing that frequency in megahertz. If all the
answer choices are the names of planets, your job is to identify a planet. If
it’s an Auto Information question and all of the answer choices start with
verbs, it’s likely you’ll be describing how to go about some type of auto
repair.
STEP 2: SIMPLIFY OR SOLVE.
This step varies quite a bit depending on the subject matter. Therefore, this
section will discuss a variety of approaches depending on the information
you are given.
Diagrams
Some technical subtest question may include a diagram. On those
questions, ask yourself:
What does the diagram represent?
Are there any important relationships depicted in the diagram?
How does the diagram help me to answer the question?
Numbers, variables, or formulas
Some technical subtest questions resemble math questions. You may be
asked to perform calculations, manipulate variables, or apply a formula
(especially on Mechanical Comprehension, but on other tests as well). You
can o en approach these questions using the same tactics you use for the
math subtests. Review chapter 5 to remind yourself of these approaches.
For each technical subtest question involving math, ask yourself:
How can I simplify the information I’m given?
Am I given a formula or expected to recall one out of my own
knowledge?
Can I backsolve, pick numbers, or guess strategically using logic, or
should I simply do the math?
Charts, graphs, or tables
Some technical subtest questions may include a graphical representation
of data. If you see a chart, graph, table, or other visual arrangement of
data, ask yourself:
How does the graph relate to the information in the question?
What are the units?
What do the axes represent?
Is there a trend or pattern in the data?
Written information
If a technical subtest question includes a few sentences of introductory
text, take a moment to paraphrase them to ensure that you understand
before you move on to Step 3.
STEP 3: MAKE A PREDICTION.
Just as on Paragraph Comprehension and Word Knowledge, having a
prediction is a great strategy for finding the right answer efficiently and not
being distracted by tempting wrong answer choices. A er all, it’s easier to
recognize the correct answer if you already have a good idea what it is.
Always try to predict unless you’re using a strategic math approach such as
Backsolving or Strategic Guessing; those strategies do not require making a
prediction. As you practice, put a sticky note or your hand over the answer
choices as you’re working through Step 2, above, to get into the habit of
predicting. By Test Day, making a prediction will be second nature, and you
will not need to cover the answer choices.
STEP 4: EVALUATE THE CHOICES STRATEGICALLY.
Got a solid prediction? Look for it among the choices.
If you don’t have a solid prediction, seek to discard wrong answer choices
that do not make sense. You might be able to eliminate choices that:
contain numbers that are obviously too large or too small
are expressed using the wrong units
belong to a different category than that you were asked for. For
example, if you are asked to name a planet, “Sirius” would be a wrong
answer because it is a star rather than a planet.
are synonyms: each ASVAB question has only one right answer, so two
answer choices that mean the same thing cannot be correct. For
example, if you are working on a Shop Information question and two of
the answer choices are “Vise Grips” and “locking pliers,” cross both
those choices off. They both refer to the same tool, so it cannot be the
case that one of those answer choices is right and the other is wrong.
BRINGING IT ALL TOGETHER
Memorize the method below as soon as possible. You don’t want to put off
learning it. You’ll have lots of content review to do in the coming chapters,
and you will want the method in place so that you can use what you learn
about the subject matter to your advantage on ASVAB questions.
THE KAPLAN METHOD FOR THE ASVAB
TECHNICAL SUBTESTS
Step 1: Identify what you are being asked for.
Step 2: Simplify or solve.
Step 3: Make a prediction.
Step 4: Evaluate the choices strategically.
Note: The method above should form your approach to General Science,
Electronics Information, Auto Information, Shop Information, and
Mechanical Comprehension questions. However, since the Assembling
Objects test requires a somewhat different skill set, we will present a
different method for the Assembling Objects test in chapter 14.
Log in to your online resources at kaptest.com/login to watch the video
instruction on mastering the technical subtests. If you haven’t yet
registered your book, see “Welcome to Your ASVAB Studies” toward the
front of this book for registration instructions.
FINAL THOUGHT BEFORE YOU DIVE IN
As you study the technical subtest material in the second half of this book,
don’t forget to periodically review the math and verbal topics in the first
half of this book. Good luck with your preparations for the technical
subtests!
CHAPTER 9
GENERAL SCIENCE
Know What to Expect
The General Science section of the ASVAB covers a grab bag of topics that
you may or may not have studied in high school or elsewhere. This subtest
covers a wide variety of material, but you’ll never be expected to know too
much about a single topic. As you study this chapter, seek first to develop a
broad overview of the subject matter, learning the broad outlines of
anything that’s completely unfamiliar and refreshing your memory about
topics that seem familiar. Then, if you have time before Test Day, you can
dig deeper into these topics.
ASVAB science topics fall into three broad categories: life science, Earth
and space science, and physical science. This chapter is divided into three
parts—one for each of those categories—each with its own set of practice
questions. As usual, we’ve included worked examples and practice
questions throughout. Also, key terms you may want to memorize are
listed in bold type.
You’ll be answering 25 questions in 11 minutes on the paper-and-pencil
version, and you are given 10 minutes for 15 questions on the CAT-ASVAB.
That means you need to be able to answer ASVAB science questions in
roughly half a minute. To help you work efficiently, use the Kaplan Method
covered in chapter 8 on every science question you encounter.
Part I
LIFE SCIENCE
NUTRITION AND HEALTH
Learning Objectives
In this section, you will learn to:
describe the role of important micro- and macronutrients in the
human body and to identify where these nutrients come from
identify some diseases that can be caused by nutrient
deficiencies
Although nutritionists themselves don’t always agree about what
constitutes a healthy diet, certain facts are clear. The human body requires
a combination of protein, carbohydrates, fat, minerals, vitamins, and fiber.
Proteins, carbohydrates, and fats (macronutrients) are necessary to
provide energy. Minerals and vitamins (micronutrients) , along with fiber,
are necessary to maintain proper bodily functions.
Proteins are necessary for the body’s maintenance, growth, and repair.
Animal proteins are contained in meat, fish, eggs, and cheese. Vegetable
proteins are found in peas, beans, nuts, and some grains.
Carbohydrates include both starches and sugars. They are major sources
of energy for the body. Starches are found in bread, cereal, rice, potatoes,
and pasta. Sugars are found in fruits, cane sugar, and beets, as well as
processed foods.
Fats also provide energy for the body. There are three types of fats:
saturated, monounsaturated, and polyunsaturated. Saturated fats can
raise bad cholesterol (LDL), but mono- and polyunsaturated fats can
actually decrease levels of bad cholesterol. Diets high in saturated fat can
lead to high cholesterol, which can cause heart disease or stroke. Sources
of saturated fats include meats, shellfish, eggs, milk, and milk products.
Sources of monounsaturated fats include olives and olive oil, almonds,
cashews, Brazil nuts, and avocados. Sources of polyunsaturated fats
include corn oil, flaxseed oil, pumpkin seed oil, safflower oil, soybean oil,
and sunflower oil.
Fiber is an important part of a healthy diet that provides bulk to help the
large intestine carry away waste matter. Good sources of dietary fiber
include leafy green vegetables, carrots, turnips, peas, beans, and potatoes,
as well as raw and cooked fruits and whole-grain foods.
Water is also essential for survival. The body loses approximately four
pints of water each day, which must be replenished. Most foods contain
water, facilitating proper water maintenance, although it is still necessary
to drink water as well! Insufficient water consumption leads to
dehydration, which can cause muscle cramps, dizziness, and, if not
remedied, even death.
Minerals in small quantities are needed for a balanced diet. Some
necessary minerals are iron, zinc, calcium, magnesium, and sodium
chloride (salt). Calcium is important for building strong teeth and bones.
Iron, on the other hand, is necessary for red blood cell development.
Minerals play many different roles in the development and maintenance of
a healthy body.
Vitamins, such as vitamins C and D, are organic compounds that are
necessary for a wide variety of physiological processes from bone hardness
to healthy gums. Fruits and vegetables are rich sources of vitamins. Vitamin
D is unique in that one of the best sources comes not from your diet, but
from the Sun. Exposure to sunlight allows your body to synthesize its own
vitamin D.
A lack of the proper amount of certain necessary nutrients in the diet can
lead to deficiency diseases. One such disease is iron-deficiency anemia,
which may cause weakness, dizziness, and headaches. It is especially
common among children, young adults, and pregnant women who do not
get enough iron in their diets. Another example of a deficiency disease is
scurvy, which is caused by a lack of vitamin C. Though at one time very
common among pirates and sailors who did not have access to fresh fruits
and vegetables, scurvy is now relatively rare.
The following table lists a selection of nutrients and their sources.
Vitamin/Mineral
Iron
Calcium
Sources
Benefits
Meat (especially liver), beans,
Allows red blood cells to transfer
whole grains
oxygen to body tissues
Dairy products like milk, yogurt,
Bone growth, muscle function
and cheese; spinach
Vitamin/Mineral
Magnesium
Potassium
Sources
Benefits
Nuts, whole grains, green leafy
Bone development, muscle and
vegetables, fortified foods
nerve function, enzyme function
Bananas, sweet potatoes, nuts
Balances fluid levels in the body
and seeds
Vitamin A
Liver, milk, eggs, carrots, spinach
Vision, immune system, cell growth
Vitamin C
Red and green peppers, citrus,
Collagen formation, immune system
broccoli
function, antioxidant (helps protect
cells from damage)
Vitamin D
Fortified milk, juice, or cereal;
Bone strength (by helping the body
body makes majority of vitamin D
absorb calcium), muscle and nerve
when exposed to sunlight
function, immune system
Take a look at how an expert test taker might approach an ASVAB question
about health and nutrition.
Question
Analysis
Question
Analysis
A pregnant woman feels dizzy
and has a headache. Which of the
Step 1: You’re given three
important facts: the woman is
following would be the most
pregnant, has a headache, and is
likely diagnosis?
feeling dizzy.
(A) iron-deficiency anemia
(B) scurvy
(C) cancer
Step 2: What condition that
causes headache and dizziness is
(D) diabetes
common in pregnant women?
Step 3: Those symptoms match
iron-deficient anemia, which is
especially common among
pregnant women.
Step 4: Select choice (A).
Now try one on your own.
If a person has high cholesterol, which one of the
following foods might his doctor suggest that he avoid?
(A) olive oil
(B) red meat
(C) almonds
(D) avocados
Explanation
A person with high cholesterol should limit the intake of saturated fat. The
only choice here that is high in saturated fat is (B), red meat. The others are
filled with healthier fats (mono- and polyunsaturated fats) that could
possibly help lower high cholesterol.
Human Body Systems and Diseases
Learning Objectives
In this section, you will learn to:
identify the general components and processes of major human
body systems, including the musculoskeletal, respiratory,
circulatory, nervous, digestive, and reproductive systems
differentiate between blood types and how they influence blood
donation
describe the roles of the main components of the brain
describe the causes and effects of common health problems
differentiate between bacteria and viruses and describe several
common illnesses caused by each
THE SKELETON AND MUSCLES
The skeleton and muscles are responsible for holding the body together as
well as for movement. Without a skeleton you would be just an immobile
mass of organs, veins, and skin. Some organisms, namely arthropods
(including insects, spiders, and crustaceans), have exoskeletons, or
external skeletons. However, vertebrate animals, including humans, have
internal skeletons, or endoskeletons.
The human skeleton contains both bone and cartilage. Bones provide the
primary support, while cartilage, which is more flexible, is found at the end
of all bones, at the joints, in the nose, and in the ears. Bones not only
provide structural support for the body and protect vital organs, but also
produce blood cells and store minerals such as calcium. Tendons, tough
fibrous cords of connective tissue, connect muscles to the skeleton.
Ligaments, another type of connective tissue, connect bones to other
bones at joints such as the elbow, knee, fingers, and vertebral column.
Here’s how an expert test taker would approach an ASVAB question about
the skeletal system.
Question
Analysis
Question
Analysis
What type of tissue would
Step 1: The question asks what
connect the humerus to the ulna?
type of tissue connects two
(A) bone
bones to each other.
(B) muscle
(C) tendon
Step 2: There is nothing to
(D) ligament
simplify.
Step 3: Make a prediction:
ligaments are connected to bone.
Step 4: (D) is the correct answer.
THE RESPIRATORY SYSTEM
Respiration—the process by which blood cells absorb oxygen and
eliminate carbon dioxide and water vapor—is performed by the
respiratory system.
When air enters through the nose, it passes through the nasal cavity,
which filters, moistens, and warms air, and then through the pharynx,
which further filters the air and aids in protection against infection. The air
then passes through the open epiglottis, which closes when swallowing to
prevent food from going down the airway, and into the trachea, which
further cleanses the air. The trachea branches into the le and right
bronchi, which are two tubes that lead to the lungs. There the bronchi
further subdivide into smaller tubes called bronchioles. Each bronchiole
ends in a small sac called an alveolus. It is in the alveolus that oxygen from
the air enters into the bloodstream via tiny blood vessels called
capillaries. The diaphragm is a system of muscles that allows breathing.
When the diaphragm causes the lungs to expand, air rushes in to fill the
space, in a process called inhalation. When the diaphragm causes the lungs
to contract, air is pushed out in an exhalation.
BLOOD AND THE CIRCULATORY SYSTEM
In conjunction with the respiratory system, the circulatory system
functions to transport oxygen throughout the body while removing carbon
dioxide. Additionally, the circulatory system transports nutrients provided
by the digestive system and clears away waste by transporting it to the
excretory system. The organ that drives the circulatory system is the heart.
The human heart is a four-chambered pump, with two collecting chambers
called atria (singular: atrium), and two pumping chambers called
ventricles. The right atrium receives deoxygenated blood from the venae
cavae (plural of vena cava), the two largest veins in the body, and passes it
to the right ventricle, which pumps the blood to the lungs through the
pulmonary artery. Blood picks up oxygen in the lungs and returns to the
le atrium via the pulmonary vein. From there it passes to the le
ventricle and is pumped through the aorta, the body’s largest artery, into
several smaller branching arteries that take it through the rest of the body.
The heart’s valves are essential to efficient pumping of the heart. When
blood is pumped out of the ventricles, valves close to prevent the blood
from flowing backward into the heart a er the contraction of the ventricles
is complete.
How blood flows from the heart to the body:
right atrium
ventricle
right ventricle
lungs
le atrium
le
body
The right side of the heart is associated with deoxygenated blood (because
the blood hasn’t gotten to the lungs yet), whereas blood coming into the
le side of the heart is oxygenated because it’s sent there from the lungs.
Heart disease (also known as cardiovascular disease) is the most
common cause of death in the United States. High cholesterol, high blood
pressure, smoking, and lack of exercise can all contribute to the
development of heart disease, which can lead to heart attack or heart
failure.
The Human Heart
The arteries carry blood from the heart to the tissues of the body. They
repeatedly branch into smaller arteries (arterioles), which supply blood to
bodily tissues via the capillaries. Arteries carry blood away from the heart
and thus must be thick-walled because they carry oxygenated blood at
high blood pressure. Only the pulmonary artery, which carries blood from
the heart into the lungs, does not contain oxygenated blood.
Veins, on the other hand, carry blood back to the heart from other parts of
the body. Veins are relatively thin-walled, conduct blood at low pressure,
and contain many valves to prevent backflow. Veins have no pulse and
carry dark red, deoxygenated blood. The lone exception is the pulmonary
vein, which carries freshly oxygenated blood from the lungs back into the
heart.
Finally, capillaries are thin-walled vessels that are very small in diameter.
Capillaries, rather than arteries or veins, permit exchange of materials such
as oxygen, carbon dioxide, nutrients, and waste between the blood and the
body’s cells through diffusion.
The Capillary System
Hypertension, also known as high blood pressure, can cause damage to
blood vessels as well as other parts of the body like the kidneys. Limiting
salt intake, maintaining a healthy weight, and exercising can help prevent
or manage hypertension.
Blood consists of cells suspended in plasma, the liquid component of
blood. There are three types of cells found in blood: red blood cells, which
are the oxygen-carrying cells; white blood cells, which fight infection by
destroying foreign organisms; and platelets, which are cell fragments that
allow blood to clot. All blood cells are created in the bone marrow, which
is located in the center of bones.
Each of these blood cell types can be measured in the blood as an indicator
of overall health. When white blood cell levels are higher than normal, that
indicates that the body is fighting off some sort of infection by either
bacteria or a virus.
It is also important to note that blood comes in four different types: A, B,
AB, and O, which can be further designated as either negative or positive.
One combination may be written as A+ or A positive, for example. The
letter designation is determined by the type of molecules (antigens) found
on the outside of the red blood cells. The positive or negative designation
is assigned based on whether or not cells have a third type of antigen
called the Rh factor. A person who has blood that is Rh-factor negative
cannot receive blood with a positive type; however, a person with positive
type blood can receive donor blood that is Rh-negative. Type O negative is
the universal donor, which means that type O negative blood can be given
to anybody. Type AB positive is the universal recipient, which means that
someone with this type of blood can receive any other type of blood.
Here’s how an expert test taker would think through an ASVAB question
about the circulatory system.
Question
Analysis
Question
Which of the following does not
contain oxygen-rich blood?
Analysis
Step 1: The question asks which
listed item does not contain
oxygen-rich blood.
Step 2: Possible answer choices
will contain three choices that do
contain oxygen-rich blood and
one (the correct answer) that
does not.
Step 3: A vague question like this
can be hard to predict, because it
doesn’t tell you if you are looking
for a blood vessel or a part of the
heart. Either way, you should
start thinking about what you
know about blood flow in the
heart and to the body.
Question
Analysis
(A) aorta
(B) le ventricle
Step 4: The aorta (A) carries
oxygenated blood away from the
(C) pulmonary vein
(D) right atrium
le ventricle (B) of the heart, so
neither of those is correct. The
pulmonary vein (C) carries
oxygenated blood to the le side
of the heart from the lungs, so
that leaves choice (D), right
atrium, as the correct answer.
THE DIGESTIVE AND EXCRETORY SYSTEMS
The digestive system is responsible for breaking down foods into material
the body can use for energy and building body tissues. The digestive tract
is essentially a long and winding tube that begins at the mouth and ends at
the anus.
The process of digestion progresses as follows:
In the mouth, the teeth and the tongue aid in mechanical digestion
(chewing), while the enzyme salivary amylase, contained in the saliva,
begins to break down starch.
From the mouth, the chewed food moves into the esophagus.
Contractions push the food down through the esophagus and into the
stomach.
In the stomach, food is mixed with gastric acids and pepsin, which help
break down protein.
Most digestion takes place in the small intestine. The small intestine is
very long, about 23 feet on average. Food is broken down completely by
enzymes produced in the walls of the small intestine, in the pancreas,
and in the liver. The acids produced by the pancreas contain lipase,
which converts fat to glycerol and fatty acids; pancreatic amylase,
which breaks down complex carbohydrates into simple sugars; and
trypsin, which converts polypeptides (the molecules that compose
proteins) into amino acids. Bile, which is produced by the liver, aids in
digestion by emulsifying fat (physically separating it into individual
molecules). All these digested substances, except for the fatty acids and
glycerol, are then absorbed in the small intestine through capillaries
that carry the blood into the liver and then throughout the rest of the
body.
In the large intestine, also known as the colon, water and minerals
remaining in the waste matter are absorbed back into the body.
Chemical waste, such as urea, excess salts, minerals, and water, are
filtered from the blood by the kidneys and secreted into the urine. Urine
is transported to the bladder from the kidneys through the ureters.
In the rectum, solid waste matter is stored. Liquid waste (urine) is stored
in the bladder.
Solid waste matter is periodically released through the anus, and urine
is released through the urethra.
The Digestive System
Study the example below to see how an expert test taker might approach a
question about the digestive system.
Question
Analysis
Question
Analysis
Where does food go a er the step
Step 1: The question is asking
where proteins begin to be
digested?
about the next step in digestion
a er digestion of proteins begins.
Step 2: This is essentially two
questions in one. First, identify
where proteins are digested.
Second, recall where food goes
a er that step.
Step 3: Recall that protein
digestion begins in the stomach
with the help of stomach acid
and pepsin. Predict where food
goes a er being in the stomach:
the small intestine.
(A) esophagus
(B) stomach
(C) small intestine
(D) large intestine
THE NERVOUS SYSTEM
Step 4: Choice (C) is correct.
The nervous system consists of the brain, the spinal cord, and the network
of billions of nerve cells called neurons, which behave like electrical wires
that send and receive signals throughout the body. The nervous system
controls the functions of the body and receives and processes stimuli from
the environment.
The nervous system consists of the central nervous system, which is
made up of the brain and spinal cord, and the peripheral nervous system,
which contains all the other neurons found throughout the body.
The main components of the central nervous system are as follows:
The cerebrum is the major part of the brain. It is thought to be the
center of intelligence, responsible for hearing, seeing, thinking, etc.
The cerebellum is a big cluster of nerve tissue that forms the basis for
the brain. It is most closely associated with balance, movement, and
muscle coordination.
The medulla, which is part of the brainstem, is the connection between
the brain and the spinal cord. It controls involuntary actions such as
breathing, swallowing, and the beating of the heart.
The spinal cord is the major connecting center between the brain and
the network of nerves. It carries impulses between all organs and the
brain and is also the control center for many simple reflexes.
The Human Brain
The peripheral nervous system can be subdivided into:
The somatic nervous system, which consists of nerve fibers that send
sensory information to the central nervous system and control
voluntary actions.
The autonomic nervous system, which regulates involuntary activity
in the heart, stomach, and intestines.
The example below walks you through the expert approach to an ASVAB
question about the nervous system.
Question
Analysis
Question
Which of the following parts of
the brain, if damaged, would
likely cause a person to have
poor balance?
Analysis
Step 1: The question asks for a
part of the brain that would affect
balance if it were damaged.
Step 2: There’s nothing to
simplify.
Step 3: Make a prediction based
on what you know about the
brain: the cerebellum is closely
related to balance.
(A) medulla
(B) spinal cord
(C) cerebellum
Step 4: Choose (C). The medulla
and spinal cord are associated
with more basic, involuntary
(D) cerebrum
functions like breathing and
reflexes, whereas the cerebrum
handles higher functions like our
intelligence, so none of these
choices fit.
THE REPRODUCTIVE SYSTEM
Human reproduction occurs when a female’s egg is fertilized by a male’s
sperm. During female ovulation, which occurs approximately every 28
days, an egg (ovum) is released from one of the ovaries and begins to
travel through the oviduct (fallopian tube) and into the uterus. At the
same time, the endometrial lining of the uterus becomes prepared for
implantation.
Male and Female Reproductive Systems
During intercourse, the penis ejaculates more than 250 million sperm,
produced in the testes, into the vagina. Some of the sperm make their way
to the uterus, where they may encounter an egg to fertilize. If the sperm
unites with the ovum, a fertilized egg (zygote) is formed, which may
implant in the uterus and eventually develop into a fetus. During
pregnancy and a er childbirth, prolactin, a hormone secreted by the
pituitary, activates the production of breast milk (lactation).
If the ovum fails to become fertilized, the uterine lining sloughs off during
menstruation. From puberty to menopause, this menstrual cycle repeats
monthly except during pregnancy.
HUMAN PATHOGENS
Some diseases, such as deficiency disorders, hypertension, and heart
disease, are caused by diet and/or lifestyle factors. Another major cause of
human disease are pathogens—disease-causing agents—such as bacteria
and viruses. Bacteria, which are single-celled organisms, are responsible
for diseases such as strep throat, staph infections, and pneumonia; these
illnesses may be treated with antibiotic medications.
On the other hand, viruses are not technically living things because they
are only able to replicate inside a host’s cells. Viral illnesses in humans
include the common cold and flu, AIDS (acquired immunodeficiency
syndrome), and herpes. These illnesses cannot be treated with antibiotics,
but may be treated with specially-designed antiviral drugs.
Both bacteria and viruses may be spread from person to person in several
different ways. Some bacteria and viruses (including the cold and flu) may
be passed through the air, wherein an infected person coughs or sneezes
and another individual inhales the pathogen. Some viruses, like HIV
(human immunodeficiency virus), can only be transmitted through contact
with infected body fluids, as in sexual intercourse or intravenous drug use.
Others, like herpes, can be spread by skin-to-skin contact. Every type of
virus and bacteria has a unique profile when it comes to how it is
transmitted and what type of cells it infects.
Luckily, many diseases caused by viruses (and a few caused by bacteria)
can be prevented through vaccination. Vaccination, also called
immunization, prevents many diseases that, not long ago, would have
been very severe if not fatal, including smallpox, polio, and the measles.
When a person receives a vaccine, a small amount of deactivated,
weakened, or partial pathogen is injected into the body, causing the
immune system to react; if the body is exposed to that pathogen in the
future, the immune system will have a quick response to it, protecting the
person from infection.
Here’s how to approach an ASVAB question about human health on Test
Day.
Question
Analysis
Which of the following illnesses
could be treated with an
Step 1: The question asks which
illness can be treated with an
antibiotic?
antibiotic.
Step 2: Antibiotics can only treat
bacterial infections, so that’s
what you’re looking for.
Step 3: It’s hard to make a
specific prediction, but you do
know you’re looking for an illness
that’s caused by bacteria.
Question
Analysis
(A) influenza
(B) anemia
(C) strep throat
Step 4: Influenza and herpes are
caused by a virus, while anemia
is caused by iron deficiency. The
(D) herpes
correct answer is (C), strep
throat, which is caused by
bacteria.
Now that you’ve gotten an overview of the human body systems and
causes of disease, try your hand at a few questions:
1. Blood pressure is generally highest in which of the
following?
(A)
(B)
(C)
(D)
veins
capillaries
arteries
lungs
2. White blood cells are produced in
(A) the heart
(B) the superior vena cava
(C) the lymph nodes
(D) the bones
3. Processing of signals from the heart and regulation
of cardiac rhythm occurs in
(A) the cerebrum
(B) the medulla, or brain stem
(C) the cerebellum
(D) the spinal cord
Explanations
1. (C) arteries Arteries pump blood away from the heart to the rest of the
body, so the blood pressure is highest in those vessels. Some veins, (A),
have such low blood pressure that they need valves to keep the blood from
flowing the wrong way! Capillaries, (B), are tiny vessels located far from the
heart, so their blood pressure is relatively low as well.
2. (D) the bones Reading the question stem carefully, home in on the key
word, “produced.” Try to make a prediction before -looking at your answer
choices, if possible. Although white blood cells are found in the blood, and
thus pass through the vena cava and heart, they are produced in the center
of bones, the marrow, so look for an answer like “marrow” or “bone.”
3. (B) the medulla, or brain stem Make a prediction. Regulation of the
heart is an autonomic (involuntary) process. It occurs in the brain stem
(medulla).
Genetics
Learning Objectives
In this section, you will learn to:
describe how genetics determine the physical characteristics of
an organism
distinguish between genotype and phenotype
recognize several health problems that are genetically inherited
Genetics is the study of heredity, the process by which characteristics are
passed from parents to offspring. The basic laws of genetics have been
understood since the late eighteenth century, when they were first
discovered by Gregor Mendel. What Mendel discovered was that in sexual
reproduction, individual heredity traits separate in the reproductive cells,
so that reproductive cells, known as gametes, have half as many
chromosomes (large strings of hereditary units) as normal cells. Normal
body cells are called diploid, and gametes are called haploid. (Think
DIploid = Double and HAploid = HAlf to help you remember it.)
In human reproduction, the female gamete (ovum) combines with the
male gamete (sperm), each of which contains 23 unpaired chromosomes
(haploid), to produce a zygote, which contains 23 pairs of chromosomes, or
a total of 46 (diploid). Meiosis is the process by which gametes are created.
Sexual reproduction by meiosis and fertilization results in a great deal of
variation among offspring.
DNA (deoxyribonucleic acid) is the molecule that contains genetic
information. It is “written” with the genetic code, a combination of
nucleotides that bind together in a specific pattern that can be “read” by
the cell to instruct it how to grow and behave. DNA is shaped in a double
helix, which looks like a ladder that is twisted along its axis.
DNA Molecule
A gene is defined as the unit of inheritance contained within the DNA of an
individual. A gene may come in several varieties, known as alleles. For
example, in the gene that determines eye color, a person may have the
allele for brown eyes or green eyes. Each of us has two alleles for every
gene, one inherited from each parent. These alleles may or may not be
alike. If the alleles are alike, that person is homozygous for that particular
gene. If the alleles are different, the person is heterozygous for that
particular gene. The sex of babies is determined by the genes contained on
the sex chromosome. In females, the two sex chromosomes are alike and
are designated as XX. In males, the sex chromosomes are heterozygous and
designated as XY.
Genetic traits are inherited independently of one another, and when
different traits are paired up during the fertilization of an egg, o en one
trait is dominant and the other is recessive. A recessive trait is only
expressed if the offspring has two copies of that trait. A dominant trait, on
the other hand, will be expressed even if only one copy (paired with a
recessive trait) is present. For example, Huntington’s disease, which causes
degeneration of nerve cells and loss of muscle control, is passed from
parent to offspring as a dominant trait, so only one copy is necessary for
the offspring to inherit the disorder. On the other hand, cystic fibrosis,
which affects the lungs, is caused by a recessive trait, which must be
inherited from both parents in order to cause the disease. Other disorders,
such as some types of cancer, Down syndrome, and color blindness, are
also caused by genetic traits.
A person’s genotype is their genetic makeup, including both dominant and
recessive alleles. A person’s phenotype is simply how their genes express
themselves in physical characteristics. Take eye color, for example. If a
woman has brown eyes, then brown eyes are part of her phenotype.
Study the following example.
Question
Analysis
Question
Analysis
Suppose that black fur in rabbits
Step 1: You’re being asked for a
is a dominant trait and that white
deduction based on a set of facts.
fur in rabbits is a recessive trait. A
black rabbit and a white rabbit
Two rabbits—one black and one
white—have a white kit.
mate and produce a white kit
(that is, baby rabbit).
Step 2: If white is a recessive
Which of the following inferences
is supported by this information?
trait, the white kit must have
inherited a white-fur allele from
each of its parents. The white
rabbit parent must have two
white-fur alleles, and one of
those alleles was passed on to
the kit. The black rabbit parent
must have a black-fur allele and a
white-fur allele, if it passed a
white-fur allele along to the kit.
Step 3: One of those insights will
show up in the answer choices.
Question
Analysis
(A) The parents’ next kit will be
Step 4: Choice (C) matches one
black.
of the deductions made earlier
(B) The white rabbit has a
and is correct. You do not have
recessive black-fur allele.
enough information to infer
(C) The black rabbit has a
recessive white-fur allele.
anything about other kits the
parents might have, so choice (A)
(D) The kit is an albino.
is wrong. Choice (B) contradicts
the information in the question
stem: you’re told that black is
dominant. There is no support for
the claim (D) that the kit displays
albinism.
Cellular Structures and Functions
Learning Objectives
In this section, you will learn to:
describe the broad outlines of cell theory
identify different types of cells
identify the structures of eukaryotic cells
understand cell growth and cell processes
Cell theory states that (1) all living things are composed of cells, (2) cells
are the basic units and structure of living things, and (3) new cells are
produced from existing cells.
Cells are classified into two categories based on the absence or presence of
a nucleus: prokaryotic and eukaryotic. Prokaryotic cells are characterized
by not having a nucleus; bacteria are one example.
Structure of a Prokaryotic Cell
Plants, animals, fungi, and protists are made up of eukaryotic cells and
characterized by having a nucleus and a more complex structure than a
prokaryotic cell. The nucleus of a eukaryotic cell contains the genetic
material of the cell. Outside the nucleus lies the cytoplasm, a substance
which surrounds the other cell structures. The cytoplasm contains many
other organelles (cell parts with specific functions). These include:
ribosomes, which produce proteins
mitochondria (singular: mitochondrion), which produce energy
endoplasmic reticulum, which is involved in the synthesis of proteins
and fats
Golgi apparatus, which “packages” proteins for use
lysosomes, which help the cell manage waste
centrosomes, which can be important in guiding the cell’s reproduction
Structure of a Eukaryotic Cell
Plant cells also have a somewhat rigid cell wall surrounding the
membrane. The cell wall provides structure and support for cells.
Some plant cells produce their own energy through the process of
photosynthesis. Photosynthesis is the process by which sunlight, carbon
dioxide, and water react to make sugar and oxygen. It serves as a source of
energy for the cells and takes place in plant cells.
Animal cells are surrounded by a semipermeable membrane which allows
for the diffusion of water and oxygen from inside the cell to the outside of
the cell and vice versa. These cells cannot produce their own energy and
rely on consuming outside sources to provide them with the tools to make
energy through cellular respiration. Cellular respiration is the process by
which the mitochondria process sugar and oxygen to produce energy,
water, and carbon dioxide. Cellular respiration serves as the energy source
for animal cells. If no oxygen is present, cellular respiration will result in
fermentation, where either lactic acid or alcohol is produced instead of
sugar.
Cell division is the process where genetic material is replicated in the
nucleus. Cell division begins in interphase, where DNA replication occurs.
This results in the replication of the chromosomes in the nucleus.
Chromosomes are tightly coiled threads of DNA composed of twin strands
called chromatids. Interphase is the longest part of cell division and is
divided into periods of cell growth and DNA replication. The cell grows in
size to accommodate the increase in chromosomes. Following interphase
is prophase. During prophase, chromatids begin to pair up with their sister
chromatids. This leads into metaphase, where the sister chromatids move
to opposite poles of the cell. During the next phase, anaphase, the
chromatids begin to pull apart into two separate poles. The cell becomes
elongated during this phase, which makes it very easy to identify. During
telophase, the two new nuclei become completely separated. The final
phase in cell division is cytokinesis, where the cytoplasm and cell
membranes complete their separation and two daughter cells are formed.
Normally, cell reproduction is closely regulated by genetic signals in the
cell that tell it when to stop reproducing; cancer occurs when the signals
are mutated and cells can grow without limit. Factors such as smoking, sun
exposure, and genetic mutations can cause damage to cells and may lead
to cancer. The most common type of cancer is skin cancer, caused by
exposure to UV rays in sunlight.
Study the example below to see how an expert test taker would approach
an ASVAB question about cellular functions.
Question
Analysis
Cellular fermentation takes place
Step 1: The question is asking
when
the circumstances during which
cellular fermentation takes place.
Step 2: There is nothing to
simplify here.
Step 3: Cellular fermentation
occurs when no oxygen is
present. When oxygen is not
present, the cell is in anaerobic
respiration and produces either
alcohol or lactic acid instead of
ATP, a molecule that stores and
transfers energy.
(A) no oxygen is present during
cellular respiration
Step 4: Based on the prediction
above, select answer choice (A).
(B) oxygen is present during
cellular respiration
(C) lactic acid is present during
cellular respiration
(D) yeast is present during
cellular respiration
Try your hand at the problem below:
In which organelle does DNA replication take place?
(A) mitochondria
(B) mitochondria
(C) nucleus
(D) endoplasmic reticulum
Explanation
Answer choice (C) is correct. The nucleus contains all genetic material. DNA
replication takes place in the nucleus during interphase. Interphase is the
longest phase of mitosis.
Ecology
Learning Objectives
In this section, you will learn to:
understand the relationship between organisms and their
physical environment
understand the relationships between living organisms
Ecology is the study of the interrelationships between organisms and their
physical surroundings. Just as biologists classify organisms according to
terminology that goes from the general to the specific, ecologists employ a
similar set of terminology:
Biosphere: The zone of planet Earth where life naturally occurs,
including land, water, and air, extending from the deep crust to the
lower atmosphere.
Biome: A major life zone of interrelated species bound together by
similar climate, vegetation, and animal life.
Ecosystem: A system made up of a community of animals, plants, and
other organisms as well as the abiotic (non-living) aspects of its
environment.
Community: The collection of all ecologically connected species in an
area.
Population: A group of organisms of the same species living in the same
region.
An ecosystem can be large or small, and can include both pristine and
highly developed areas. An ecosystem contains a community, and this
community may contain many populations of organisms. The various
populations within a community fall into one of several roles in the food
chain.
Producers (mainly plant life): Also known as autotrophs, they make
their own food via photosynthesis.
Decomposers (bacteria and fungi): Also known as saprotrophs, they
break down organic matter and release minerals back into the soil.
Scavengers (many insects and certain vertebrates, such as vultures and
jackals): These animals exhibit characteristics of decomposers by
consuming refuse and decaying organic matter, especially carrion, or
decaying flesh. Similar organisms called detritivores consume the
small pieces of decaying organic matter called detritus that are too
small for most scavengers to want.
Consumers (most animals): Also known as heterotrophs, refers to
animals that consume other organisms to survive. Consumers are
divided into three types:
Primary consumers: Also known as herbivores, they subsist on
producers, such as plants. Examples include grasshoppers, deer, cows,
and rabbits.
Secondary consumers: Also known as carnivores or predators, they
subsist mainly on primary consumers. Examples of secondary
consumers include birds of prey (such as owls and falcons), foxes, and
snakes. Some secondary consumers are also omnivores, meaning they
consume producers and consumers as well. Examples include chickens,
rats, some lizards, and sea otters.
Tertiary consumers: Also known as top carnivores, they are capable of
eating secondary consumers. Many tertiary consumers are also
omnivores. Examples include lions, wolves, and sharks, as well as
human beings.
The diagram below shows roughly the relationships between these groups
in an ecosystem: Hierarchy of Consumers
Food chains are a basic way to see the levels in an ecosystem. However,
food webs can show more complex relationships that exist amongst the
levels. In the example below, the organism to which an arrow points might
eat the organism on the other end of that arrow.
A Food Web
Study this example of a solid approach to an ecology question.
Question
Analysis
Which of the following is the term
Step 1: The question is asking for
for the zone that extends from
the Earth’s crust through the
the name of the zone containing
all life on Earth.
lower atmosphere and which
encompasses all life on Earth?
Step 2: Not much to simplify
here.
Question
Analysis
Step 3: The question describes
the biosphere.
(A) biome
Step 4: Based on the prediction
(B) biosphere
above, select answer choice (B).
(C) ecosystem
The biosphere begins in the deep
(D) stratosphere
crust of the Earth and includes all
areas where life can exist—land,
water, and air. An ecosystem and
a biome are smaller areas. The
stratosphere is higher than the
lower atmosphere.
Try your hand at the problem below:
Which of the following is a decomposer?
(A) vulture
(B) fly
(C) oak tree
(D) bacteria
Explanation
Choose (D). Bacteria are considered a decomposer because they break
down dead matter and release it back to the soil as minerals. Flies and
vultures would be scavengers, and a tree would be an autotroph.
The Classification of Living Things
Learning Objective
In this section, you will learn to:
describe the major classifications of life and how they differ
All living things fall into a careful classification scheme that goes from the
broadest level of similarity (domain) to the narrowest (species). The
classification scheme has seven different levels. They are: Domain: the
broadest category; there are only three domains. This level of classification
is a fairly recent change to the classification system. You may not have
been taught about domains in school, and you may or may not see them
on the ASVAB.
Kingdom: which contains several related phyla.
Phylum: which contains several related classes.
Class: which contains several related orders.
Order: which contains several related families.
Family: which contains several related genera.
Genus: which contains several related species.
Species: which contains organisms so similar that they can only reproduce
with one another to create viable fertile offspring.
For example, this is the classification of human beings: Domain —
Eukaryota
Kingdom — Animalia
Phylum — Chordata
Class — Mammalia
Order — Primates
Family — Hominidae
Genus — Homo
Species — Sapiens
Remember: Domain Kingdom Phylum Class Order Family Genus
Species.
Here’s a mnemonic to help you: Dear King Philip Came Over For
Good Soup.
(Remember, Domain is a fairly recent addition to the classification
system, so you may or may not see it on the ASVAB.)
The three domains are:
Eukaryota: All living things whose cells have nuclei are in this domain.
Almost all multi-celled organisms (including plants, animals, and fungi) are
in this domain.
Bacteria and Archaea: Both of these domains contain single-celled
organisms whose cells do not have nuclei. Living things in the two domains
are distinguishable by metabolic and chemical differences.
The five or six kingdoms are:
Kingdom
Description
Monera (sometimes broken
Includes bacteria, cyanobacteria (blue green algae), and
into two kingdoms, one of
primitive pathogens. Considered the most primitive kingdom,
which belongs to domain
it represents prokaryotic (as opposed to eukaryotic) life forms
Bacteria and one of which
—that is, the cells of Moneran organisms do not have distinct
belongs to domain Archaea)
nuclei.
Kingdom
Protista
Description
Protista are the simplest eukaryotes (that is, their cells have
nuclei). Includes protozoa, unicellular and multicellular algae,
and slime and water slime molds. Ancestor organisms to
plants, animals, and fungi; many can move around by means of
flagella. Some are also photosynthetic.
Fungi
Includes mushrooms, bread molds, and yeasts. Fungi lack the
ability to photosynthesize; they are called decomposers,
breaking down and feeding on dead protoplasm (extracellular
digestion).
Plantae
Have the ability to photosynthesize, so they are called
producers. There are four major phyla: Bryophyta, or mosses;
Tracheophyta, which have vascular systems; gymnosperms;
and angiosperms.
Animalia
Produce energy by consuming other organisms, so they are
called consumers. Can be either vertebrates (which belong to
phylum Chordata) or invertebrates such as mollusks,
arthropods, sponges, coelenterates, worms, etc. Human beings
belong to the kingdom Animalia.
There are many, many phyla (the plural of phylum), classes, orders,
families, genera (the plural of genus), and species. If you have additional
time before Test Day and you have mastered all of the other subject tests
and maximizing your General Science score is crucial to your career goals,
you may choose to use Internet sources to learn more about some of the
largest phyla, classes, etc. Otherwise, that study is unlikely to be the best
use of your time.
Study how an expert test taker would approach a general science question
about the classification of living things:
Question
Analysis
Mammals are part of the
Step 1: The question is asking
kingdom
you to determine which kingdom
mammals belong to.
Step 2: There is nothing to
simplify here.
Step 3: Mammals are animals;
they belong to kingdom
Animalia.
(A) Animalia
(B) Mammalia
Step 4: Based on the prediction
above, you would select answer
(C) Protista
choice (A).
(D) Monera
Try one on your own.
Not including domains, the correct order of the
categories of taxonomy, from most specific to most
general, is:
(A) Species, Genus, Family, Order, Class, Phylum,
Kingdom
(B) Kingdom, Phylum, Class, Order, Family, Genus,
Species
(C) Kingdom, Phylum, Order, Class, Family, Genus,
Species
(D) Species, Genus, Order, Family, Class, Phylum,
Kingdom
Explanation
“Species” is the most specific category in taxonomy and “Kingdom” is the
most general (not including domains), so choice (A) is correct. Choice (B)
lists the categories from largest to smallest. Choice (C) almost does the
same but confuses Order and Class. Choice (D) is incorrect because it
switches the places of “Order” and “Family.”
Life Science Practice Questions
1. Which of the following describes the proper pathway of blood
through the heart?
(A) vena cava → right atrium → right ventricle → pulmonary artery
→ pulmonary vein → le atrium → le ventricle → aorta
(B) vena cava → right atrium → right ventricle → pulmonary vein →
pulmonary artery → le atrium → le ventricle → aorta
(C) vena cava → right atrium → le atrium → pulmonary artery →
pulmonary vein → le atrium → le ventricle → aorta
(D) vena cava → right atrium → le atrium → pulmonary vein →
pulmonary artery → le atrium → le ventricle → aorta
2. Most human digestion takes place in the
(A)
(B)
(C)
(D)
esophagus
stomach
small intestine
large intestine
3. Which blood type can be donated to anyone?
(A)
(B)
(C)
(D)
A positive
B negative
O negative
AB positive
4. A typical human gamete contains
(A) 2 chromosomes
(B) 23 chromosomes
(C) 46 chromosomes
(D) 92 chromosomes
5. Which of the following is an example of a primary consumer?
(A) moss
(B) mushroom
(C) jackal
(D) deer
6. How many domains are recognized in taxonomy?
(A) 3
(B) 5
(C) 7
(D) 9
7. Which of the following foods is a good source of fiber?
(A) oils
(B) fruits and vegetables
(C) dairy products
(D) meat and seafood
8. Which components of a prokaryotic cell produce proteins?
(A) ribosomes
(B) mitochondria
(C) lysosomes
(D) centrosomes
9. A zygote is a
(A) diseased cell
(B) mutated male reproductive cell
(C) female reproductive cell
(D) fertilized egg
10. Which of the following describes how the process of immunization
takes place?
(A) A highly active form of a pathogen is injected, causing the
formation of strong antibodies that will fight off the injected
pathogen and remain in the blood stream to fight off future
infections.
(B) Synthetic antibodies are injected into the bloodstream that
will persist in the body and fight off future infections.
(C) A small amount of a deactivated pathogen is injected, causing
the immune system to react so that if an active form of the
pathogen is encountered in the future, the immune system will
respond quickly.
(D) Chemicals that can destroy a pathogen's ability to reproduce
are injected into the bloodstream.
Answers and Explanations
LIFE SCIENCE PRACTICE QUESTIONS
1. A
To make a prediction on this question, think about what kind of blood
(oxygenated or deoxygenated) flows into and out of the heart.
2. C
The small intestine is the largest digestive organ and does the most
work in breaking down food into materials the body can use.
3. C
Type O negative blood, also known as the “universal donor” type, can
be donated to anyone.
4. B
A typical human gamete contains half the number of chromosomes as a
normal cell, or 23.
5. D
A deer is an example of a primary consumer, that is, an animal that
consumes only vegetation.
6. A
There are three domains in taxonomy: Eukaryota, Bacteria, and Archaea.
7. B
Sources of dietary fiber include fruits and vegetables, whole grains, and
legumes.
8. A
The primary function of ribosomes is to produce proteins. Mitochondria
produce energy, lysosomes help a cell manage waste, and centrosomes
are important in a cell's reproduction.
9. D
When a sperm unites with an ovum, the product is a fertilized egg, which
is called a zygote.
10. C
Immunization uses a deactivated form of a bacterial or viral pathogen.
Though inactive, this pathogen triggers the formation of antibodies that
attack it, thus "training" the immune system to respond quickly should
the active pathogen be introduced in the future.
Part II
EARTH AND SPACE SCIENCE
Earth and space science is the study of the Earth and the universe around
it. For purposes of the ASVAB, it’s helpful to know a few facts about our
planet and the solar system in which it travels.
GEOLOGY
Learning Objectives
In this section, you will learn to:
identify the layers of the Earth and types of rocks
describe the general principles of plate tectonics
describe the composition of the Earth
Geology is the science that deals with the history and composition of the
Earth and its life, especially as recorded in rocks.
STRUCTURE OF EARTH
In part by studying rocks, scientists have been able to determine that the
Earth is made up of three layers. The outermost layer, or crust, comprises
roughly one percent of the total volume of the Earth. It varies in thickness
from 10 kilometers to as much as 100 kilometers. Beneath the crust lies the
mantle, which comprises more than 75 percent of the Earth’s volume.
Roughly 3,000 kilometers thick, the mantle contains mostly iron,
magnesium, and calcium, and is much hotter and denser than the Earth’s
surface because temperature and pressure inside the Earth increase with
depth.
At the center of the Earth lies the core, which is nearly twice as dense as
the mantle because its composition is metallic (iron-nickel alloy) rather
than stony. The Earth’s core contains two distinct parts: a 2,200-kilometerthick liquid outer core and a 1,300-kilometer-radius solid inner core.
Structure of the Earth
PLATE TECTONICS
As noted, the interior of the Earth is quite hot, somewhere between 3,000°C
and 4,000°C. This heat is generally prevented from escaping thanks to the
solid rock in the Earth’s upper mantle and crust. The crust and the rigid
upper part of the mantle (the lithosphere) consist of approximately 30
separate pieces called plates. These plates move very slowly upon the
more movable mantle beneath (the asthenosphere), and this has caused
the continental landmasses to dri slowly apart over the course of
hundreds of millions of years.
Along the edges of these plates are fault lines. (Fault lines are simply
places where the plates slide relative to each other.) When plates slide
relative to each other along fault lines, earthquakes can occur. When an
earthquake occurs, scientists use the Richter scale or the moment
magnitude scale to measure its intensity. The Richter scale is perhaps
more familiar to most people. The Richter scale begins at 1, with each
larger integer representing a magnitude that is about 10 times greater than
the preceding step.
TYPES OF ROCKS
The Earth’s rocks fall into three categories, based upon how they are
formed.
Rock type
Igneous
How it’s formed
Examples
Formed from the hardening of molten rock, or magma, which is
Granite,
called lava when it reaches the surface of the Earth
pumice,
basalt,
obsidian
Sedimentary
Formed by the sedimentation, or gradual depositing, of small
Shale,
bits of rock, clay, and other materials. Over time this deposited
sandstone,
material becomes cemented together. Most fossils are found in
gypsum,
sedimentary rocks.
dolomite,
coal
Rock type
Metamorphic
How it’s formed
Examples
Formed when existing rock material is altered through
Marble,
temperature, pressure, or chemical processes
slate,
gneiss,
quartzite
GEOLOGIC TIME SCALE
Most of what is known about the history of our planet has been learned by
studying the fossil record found in sedimentary rock. By studying rocks, we
now know that the Earth is approximately 4.6 billion years old, and that for
most of that time, very few fossil traces were le . This is why the period
from 4.6 billion years to 570 million years ago is called the Precambrian
eon, meaning the period before the fossil record began. It turns out,
however, that early geologists who studied the Precambrian eon were
unable to recognize early, primitive fossils, and in fact life first appeared on
Earth as early as 3.5 billion years ago!
Here’s how a well-prepared test taker would approach a question about
geology on Test Day.
Question
Analysis
Studies of the Precambrian eon
Step 1: The Precambrian eon
have shown that life first
appeared on Earth approximately
allowed scientists to narrow
down the time frame for life
formation.
Question
Analysis
Step 2: The Precambrian eon
ranges from 4.6 billion to 570
million years ago.
Step 3: The correct number
should be within the range of the
Precambrian eon.
(A) 570 million years ago
(B) 3.5 billion years ago
Step 4: Based on the prediction
above, select answer choice (B).
(C) 4.6 billion years ago
(D) 5 billion years ago
Now try your hand at the problem below.
Which of the following is an igneous rock?
(A) marble
(B) gypsum
(C) pumice
(D) coal
Explanation
Choice (C) is correct. Pumice comes from volcanic rock when it cools very
quickly on the surface. The small air bubbles formed in it are visible to the
naked eye. The bubbles give it its lightweight feel and increase its
usefulness in many everyday products.
Cycles in Earth Science
Learning Objectives
In this section, you will learn to:
identify the stages of the water cycle
identify the stages of the carbon cycle
There are several biogeochemical cycles. They all work in similar fashion
in that the element or compound is released in the air and returned to
the ground. The two basic cycles this section will focus on are the water
cycle and the carbon cycle.
The water cycle is also known as the hydrologic cycle. It involves the
movement of water in all states of matter (solid, liquid, and gas) through
the atmosphere and back to the Earth. As water from the surface of the
ocean and from other bodies of water evaporates (becomes a gas), it
rises into the atmosphere. Water also evaporates into the atmosphere
from the leaves of plants; this process is known as transpiration. This
water vapor condenses to form clouds. When the clouds become too
heavy, they release precipitation in the form of a solid (snow and ice) or
a liquid (rain). Some of the water that accumulates on the surface will
travel down in the form of snowmelt or surface runoff and return to the
ocean via rivers and streams. The rest of the water is absorbed into the
Earth’s surface and travels to the water table (a process known as
infiltration). The water table serves as a reservoir and can be drawn
upon through the digging of wells.
The Water Cycle
Carbon is one of the most common elements on our planet. The carbon
cycle helps maintain Earth’s ecosystem. Carbon gas exchange is
important in maintaining a breathable atmosphere. Carbon is released
through human emissions (manufacturing) and respiration. Respiration
results in the release of carbon dioxide waste products into the
atmosphere; an animal’s breathing is one example. Respiration release is
due to human release as well as release from decomposing plant and
animal life. Carbon gathers in the atmosphere and is reabsorbed through
plants (land and ocean) and soil.
The Carbon Cycle
Study this example of an ideal Test Day approach to this question about
the carbon cycle.
Question
Analysis
Which of the following is a way
Step 1: Think of the ways that
in which carbon is released into
the atmosphere?
carbon is released into the
atmosphere.
Question
Analysis
Step 2: It is released through
respiration, decomposition, and
manufacturing.
Step 3: The correct answer
should discuss one of those
possibilities.
(A) pine trees engaging in
Step 4: Based on the prediction
photosynthesis
above, select answer choice (C).
(B) sediment settling in the
ocean(C) dead algae
decomposing
(D) new plants growing in a
forest
Now try one on your own.
During the water cycle, water enters the atmosphere
as a gas through
(A) transpiration
(B) condensation
(C) precipitation
(D) seepage
Explanation
The correct answer is (A). Water enters the atmosphere through the
process of transpiration and evaporation. Transpiration specifically refers
to water movement through plants. Condensation happens when water
vapor condenses together to form precipitation, which then falls back to
the Earth as rain or snow. Seepage is the movement of water through soil.
Meteorology
Learning Objectives
In this section, you will learn to:
identify layers of the Earth’s atmosphere
describe different types of fronts and clouds
Meteorology is not just the study of weather, but of the atmosphere and
atmospheric phenomena in general.
EARTH’S ATMOSPHERE
The first thing you should know is that there are several layers to the
atmosphere, beginning here on the surface of the Earth and continuing
up several thousand kilometers above us. The layers are:
Troposphere: The troposphere is the lowest level of the atmosphere,
where all weather takes place; it is a region of rising and falling packets of
air. Depending on the latitude and the season, it can range from 6 to 17
kilometers thick. Most of the air surrounding the Earth, which is roughly
79 percent nitrogen and 21 percent oxygen, is found in the troposphere.
Stratosphere: Above the troposphere is the stratosphere, where airflow
is mostly horizontal. The thin ozone layer in the upper stratosphere has a
high concentration of ozone, a particularly reactive form of oxygen. This
layer is primarily responsible for absorbing the ultraviolet radiation from
the Sun. As you enter the stratosphere, the temperature is about −60°C.
Mesosphere: Above the stratosphere is the mesosphere, which extends
to about 90 kilometers above the Earth. As you enter the mesosphere, the
temperature starts to drop again, to as low as −90°C. This is where we see
“falling stars,” meteoroids that fall to the Earth and burn up in the
atmosphere.
Thermosphere: Beyond the mesosphere, temperatures actually increase
with altitude in the thermosphere because there is little matter to deflect
solar radiation. Temperatures as high as 2,000°C have been recorded in
the thermosphere.
Earth’s Atmosphere
FRONTS
Differences in air pressure cause wind and the movement of air masses of
different temperatures toward each other. When a warm air mass
overtakes a cold air mass, you have a warm front. As the warm air
advances, it rides over the cold air ahead of it, which is heavier. As the
warm air rises, the water vapor in it condenses into clouds that can
produce rain, snow, sleet, or freezing rain—o en all four.
When a cold air mass overtakes a warm air mass, you have a cold front.
Most cold fronts are preceded by a line of precipitation as they roar
across an area. However, some cold fronts produce very little or no
precipitation as they move. The only sign that a front has moved through
your area is a sudden change in winds and temperature.
Sometimes two air masses meet and neither is displaced. Instead, the
two fronts push against each other in a stalemate. This is called a
stationary front. Stationary fronts o en cause cloudy, wet weather that
can last a week or more.
CLOUDS
Clouds come in different varieties based on their shape, size, and
altitude. The three main types are:
Stratus clouds are low-hanging, broad, flat clouds that blanket the sky.
The lowest of low clouds, when they occur on the ground, are called fog.
Dark stratus clouds indicate that rain will soon occur.
Cumulus clouds are massive clouds that are puffy, like popcorn, with
relatively flat bottoms and rounded tops. When cumulus clouds darken,
you can expect heavy rain.
Cirrus clouds are the thin, wispy clouds that occur much higher in the
atmosphere, at elevations of 20,000 feet or more.
Study the following example, which illustrates an expert approach to a
meteorology question.
Question
Analysis
The weather report indicates a
Step 1: Think of what happens
warm air front is moving in.
Which of the following is most
when a warm front comes in.
likely to occur as a result of that
warm air front?
Step 2: A warm front forms
when warm air overtakes a cold
air mass. Warm air is heavier
than cold air and rises.
Step 3: When warm, heavy air
rises, clouds will form. Clouds
mean precipitation, so the
answer choice will involve
precipitation.
Question
Analysis
(A) a sudden change in
Step 4: Based on the prediction
temperature
above, select answer choice (B).
(B) freezing rain
(C) hurricanes
Warm air fronts generally result
in some form of precipitation,
(D) weather stalemate
though not a full-blown storm
like a hurricane (which is a
specialized storm that develops
over warm ocean water), (C). A
sudden change in temperature,
(A). is the result of a cold air
front and a stalemate, (D). is
caused by a stationary front.
Try one on your own.
The sky is filled with dark, puffy clouds, and there is a
thunderstorm approaching. What type of clouds are
you seeing?
(A) cirrus
(B) stratus
(C) cumulus
(D) stratocumulus
Explanation
The correct answer is (C). Cumulus clouds are o en referred to as
thunderheads. They have high fluffy peaks that are perfect for generating
static electricity and producing thunderstorms. A few scattered cumulus
clouds are usually not a threat of a storm, but if several groups of them
converge, they could produce heavy rain, thunder, and lightning.
Our Solar System
Learning Objectives
In this section, you will learn to:
understand the structure of the solar system
understand the relationship of the Earth to other planets and
solar bodies
understand how Earth’s position relative to the Sun produces
Earth’s seasons
Our solar system consists of one star, which we call the Sun, eight planets
and all their moons, several thousand minor planets called asteroids, and
an equally large number of comets.
THE SUN
Our Sun is classified as a G2V star, or yellow dwarf. G2 stars are
approximately 6,000°C at the surface, are yellow, and contain many
neutrally charged metals such as iron, magnesium, and calcium. The “V”
indicates that the Sun is a dwarf star, or fairly small by the standards of
stars. The Sun’s age is calculated to be around 4.7 billion years, which is
only slightly older than the Earth itself.
Although a dwarf in comparison to other stars, the Sun contains almost
99.9 percent of the mass of our solar system. Like all stars, the Sun is a
gigantic ball of superheated plasma, kept hot by atomic reactions
emanating from its center. The temperature at the core of our Sun is
thought to be about 15,000,000°C; temperatures at the surface range
between 4,000° and 15,000°C. The diameter of the Sun is about 1.4
million kilometers, or more than 100 times that of Earth, and its surface
area is approximately 12,000 times that of Earth.
THE PLANETS AND OTHER PHENOMENA
The four planets closest to the Sun—Mercury, Venus, Earth, and Mars—
are called terrestrial planets, meaning they are similar to our own
planet in composition, with inner metal cores and surfaces of rock. Earth
and Mars are the only terrestrial planets that have moons of their own,
although the moons of Mars are much smaller than our own Moon. Earth
is the largest of the terrestrial planets.
The four planets beyond Mars—Jupiter, Saturn, Uranus, and Neptune—
are referred to as the outer planets. They also all have rings, most
notably so on Saturn. The rings of Saturn, and most likely the other
planets as well, are composed mostly of ice crystals. Pluto, once
considered the ninth planet, is no longer categorized by scientists as a
true planet. You may have learned a mnemonic (or memory trick) for the
planets in school; here’s one that allows for the omission of Pluto: My Very
Educated Mother Just Served Us Nachos. (In the diagram that follows,
Pluto is included, but remember that it is no longer considered a planet.
Also, note that the diagram that follows is not drawn to scale.)
The Solar System
In addition, the solar system contains thousands of small bodies such as
asteroids and comets. Smaller fragments of asteroids and particles shed
by comets are known as meteoroids, and when they fall into the Earth’s
gravitational field, they are seen as “falling stars,” called meteors, as they
burn up in the Earth’s mesosphere. Those
meteoroids that make it to the Earth’s surface are called meteorites. A
belt of asteroids lies between Mars and Jupiter. The Kuiper Belt, a much
larger collection of asteroids and other objects le over from the
formation of the solar system, lies beyond the known planets.
Comets are sometimes called “dirty snowballs” or “icy mudballs.” They
are a mixture of ices (both water and frozen gases) and dust that for some
reason didn’t get incorporated into planets when the solar system was
formed. Comets are invisible except when they are near the Sun. When
they are near the Sun and active, comets have highly visible tails, up to
several hundred million kilometers long, composed of plasma and laced
with rays and streamers caused by interactions with the solar wind.
By far the most important body in the solar system aside from the Sun, as
it relates to life on Earth, is our own Moon. Because of the gravitational
pull that exists between the Moon and Earth, we have tides. High tides
occur twice a day, when the Moon is at the points closest to and farthest
from the affected mass of water. It is suspected that life would never have
evolved on land without the constant ebbing and flowing of the oceanic
tides on coastal areas.
Earth orbits the Sun once per year. Because the Earth is somewhat tilted
on its axis, the northern pole is tilted toward the Sun and the southern
pole is tilted away from it for part of the year. That portion of the year is
winter in the northern hemisphere and summer in the southern
hemisphere. For part of the year that situation is reversed: that period is
winter in the northern hemisphere and summer in the southern
hemisphere. In between summer and winter, the Earth is tilted so that
neither the northern pole nor the southern pole is pointing toward the
Sun. These periods are spring and fall. Study the diagram that follows.
Earth’s Seasons
Imagine how terrified ancient humans must have been when their view of
the Sun or the Moon became partially or completely obscured during an
eclipse. Today we understand how eclipses occur and can predict them
well in advance.
A solar eclipse occurs when the Moon passes directly between the Earth
and the Sun during daylight hours. The relatively small shadow cast by
the Moon onto the surface of the Earth can either partially or totally
obscure the Sun. Because the Moon is moving in its orbit around the
Earth and the Earth is rotating on its axis, solar eclipses are brief and
move across the face of the Earth rapidly.
A lunar eclipse occurs when the Earth passes directly between the Sun
and the Moon and casts a shadow on the Moon. Therefore, a lunar eclipse
can be seen from any place on Earth where the Moon is above the
horizon. Like solar eclipses, lunar eclipses can be either partial or total.
Because the Earth has a much larger shadow than does the Moon, lunar
eclipses last much longer than their solar counterparts.
Study this example of how an expert test taker would approach an ASVAB
question about the solar system.
Question
Analysis
Which of the following is a
Step 1: The Earth is a terrestrial
characteristic of terrestrial
planet. What are its major
planets?
characteristics?
Step 2: The Earth has a solid,
rocky surface. There are many
layers to it that include a solid
inner core.
Step 3: The answer choice will
list one of those characteristics.
(A) an inner core made of ice
crystals
Step 4: Based on the prediction
above, select answer choice (C).
(B) a surface temperature similar
Terrestrial planets have an inner
to that of Earth
core of metal and a rocky
(C) an inner core of metal
(D) a surface composed of gases
surface. Outer planets have
inner cores of ice crystals.
Try this one on your own.
A “falling star” is also known as a
(A) meteor
(B) asteroid
(C) comet
(D) meteorite
Explanation
The correct answer is (A). A “falling star” is a meteor seen when a
meteoroid is burning up in the Earth’s atmosphere. If the meteroid
reaches the surface of the Earth, it is then called a meteorite.
Earth and Space Science Practice
Questions
1. The ozone layer is found in the
(A)
(B)
(C)
(D)
troposphere
stratosphere
mesosphere
thermosphere
2. What is the layer that is located immediately beneath Earth's
crust?
(A)
(B)
(C)
(D)
inner core
plates
mantle
outer core
3. The clouds that occur at the highest altitude are called
(A) cirrus
(B) cumulus
(C) nimbus
(D) stratus
4. The Kuiper belt is __________?
(A) a group of meteors that orbit around the earth
(B) a collection of asteroids and other objects le over from the
formation of the solar system
(C) a layer of Earth's atmosphere
(D) a grouping of asteroids that orbit the sun between Mars and
Jupiter
5. Which of the following is most responsible for the oceanic tides?
(A) the gravitational pull of the Sun on the Earth
(B) the gravitational pull of the Moon on the Earth
(C) the heat of the Sun
(D) the magnetic pull of the poles
6. Oxygen makes up approximately ___________ percent of Earth's
atmosphere.
(A) 10
(B) 21
(C) 78
(D) 90
7. The Richter scale is used to measure the intensity of ___________.
(A) hurricanes
(B) blizzards
(C) earthquakes
(D) tornadoes
8. The sequence of the movement of water in the hydrologic cycle is
(A) evaporation → transpiration → condensation →
runoff/infiltration → precipitation
(B) runoff → condensation → infiltration →
evaporation/transpiration → precipitation
(C) precipitation → evaporation/transpiration → condensation →
runoff/infiltration
(D) precipitation → runoff/infiltration → evaporation/transpiration
→ condensation
9. Granite is an example of what type of rock?
(A) compound
(B) igneous
(C) metamorphic
(D) sedimentary
10. Earth is somewhat shielded from harmful ultraviolet radiation by
the
(A) Van Allen belt
(B) thermosphere
(C) ozone layer
(D) troposphere
Answers and Explanations
EARTH AND SPACE SCIENCE PRACTICE QUESTIONS
1. B
The ozone layer is found in the upper stratosphere.
2. C
The mantle lies beneath Earth's crust.
3. A
Cirrus clouds are found at the highest altitude of all clouds.
4. B
There is a group of asteroids that orbit the sun between Mars and
Jupiter, but the Kuiper belt is located beyond the outermost known
planets.
5. B
The oceanic tides are caused by the gravitational pull of the Moon on
the Earth.
6. B
Oxygen accounts for approximately 21% of Earth's atmosphere.
Nitrogen makes up about 78% of the atmosphere.
7. C
The Richter scale, like the moment magnitude scale, is a logarithmic
measure of the intensity of earthquakes. An increase of 1 unit on the
Richter scale represents an increase by a factor of 10 in the intensity of
an earthquake.
8. D
Precipitation from the sky falls to the ground, where it either becomes
surface runoff or infiltrates into the ground. Evaporation from bodies
of water or transpiration from plants causes water vapor to rise into
the sky, where it condenses to form clouds and the cycle begins again.
9. B
Granite and other rocks formed by the hardening of molten magma
are classified as igneous rocks.
10. C
The ozone layer, which is between the stratosphere and mesosphere,
is primarily responsible for absorbing much of the ultraviolet radiation
from the sun.
Part III
PHYSICAL SCIENCE
Scientists would know very little about our solar system without an
understanding of physics and chemistry, collectively known as the
physical sciences. This section will cover those two disciplines as well as
the system of measurement used in both.
Measurement
Learning Objective
In this section, you will learn to:
employ the common units and basic conventions of the metric
system
relate the major temperature scales (Fahrenheit, Celsius, and
Kelvin)
Scientists don’t use British measurement units such as ounces, miles, and
gallons; instead, they use the metric system. The metric system has been
used throughout most of this chapter, but it’s time for a more detailed
examination. The key idea of the metric system is to designate one base
unit for every kind of measurement, and then make bigger or smaller units
by adding prefixes to it (groups of letters added to the beginnings of words,
like anti– or pro–). For example, the base unit for length in metric is called
the meter (m), which is just over a yard (about 39.4 inches).
To measure small things like firearm ammunition or large things like the
distance between cities, a prefix is added. Milli– means
, so a
millimeter (mm) is
the size of a meter. A 9 mm handgun like the
Beretta M9 (the US military’s standard sidearm) fires rounds that are .009 m
in bullet diameter. A centimeter (cm) is 10 times as big as a millimeter, and
there are about 2.54 cm in one inch. A kilometer (km) is 1,000 meters.
Metric measurements typically have two- or three-letter symbols (like mm,
cm, and km), which are usually the first letter of the prefix followed by the
first letter of the base unit.
Prefix
Symbol
Value relative to base
unit
mega
M
106 or 1,000,000
kilo
k
103 or 1,000
hecto
h
102 or 100
deka
da
101 or 10
base (no
—
1
deci
d
10-1 or
centi
c
10-2 or
milli
m
10-3 or
or 0.001
micro
µ (the Greek letter mu, to avoid confusion with
10-6 or
or
“mega”)
0.000001
prefix)
or 0.1
or 0.01
The most common prefixes (and the most likely to come up on the ASVAB)
are milli–, centi–, kilo–, and sometimes mega–. The other prefixes on the
table are included for the sake of completion, but it’s not important to
memorize them, nor other prefixes beyond those listed here. Know both
the prefix names as well as their symbols, as the symbol (for example, km
for kilometer) is more likely to come up in a calculation question than the
name.
Applying the prefix scheme to other measurements, mass is measured in a
base unit of grams (g). Therefore, large objects can be measured in
kilograms (kg), and very small things can be measured in milligrams
(mg); for example, the amount of certain minerals and nutrients per
serving as listed on a food package’s nutritional information tend to be in
milligrams. There are approximately 28.3 grams in an ounce, and a mass of
one kilogram will have a weight of approximately 2.2 pounds (at the
surface of the Earth).
Volume is the measurement of three-dimensional space. A cube (square
box) which is one centimeter on a side can be called just that: a cubic
centimeter (cc); but it can also be called a milliliter (mL). The definition of
the milliliter automatically implies the liter (L): the prefix means a milliliter
is one-thousandth of a liter, which is the same as saying a liter is equal to
one thousand milliliters. A liter is equal to slightly more than a quart in
liquid measure, or about 33.8 ounces, with about 3.79 liters in a gallon.
Time is measured in seconds (s) and metric prefixes are used when
smaller units are required (as in milliseconds). However, minutes (min)
and hours (h) are also common.
Finally, the metric system equivalent of temperature is the Celsius scale,
also known as degrees centigrade. According to the Fahrenheit scale,
which is more familiar to most people in the United States, water freezes at
32°F and boils at 212°F. On the Celsius scale, water freezes at 0°C and boils
at 100°C. The general equations for converting from the Fahrenheit scale to
the Celsius scale, or vice versa, are as follows:
Finally, there is one other temperature scale commonly used by scientists,
known as the Kelvin scale, or the absolute zero scale. Absolute zero is the
temperature at which matter has no heat and its molecules are completely
still; in theory, absolute zero is the lowest temperature possible. On the
Kelvin scale, absolute zero is set at 0 K, which is equal to −273°C.
Otherwise, the Kelvin scale uses the same increments as degrees Celsius,
so that water freezes at 273 K and boils at 373 K. Note that there is no
degree symbol when writing out temperatures in the Kelvin scale.
The unit types discussed here are not exhaustive. Different base units come
up in different areas of science, but the beauty of metric standards is that
the value of each prefix is a constant. Metric prefixes will be applied in new
contexts elsewhere in this chapter, and again in chapter 10: Electronics
Information.
Question
Analysis
Question
Analysis
In a chemistry lab, the
experimental procedure says to
Step 1: The question asks for the
value of 50 mL converted to L
add 50 mL of room temperature
units.
water to a beaker. How many
liters are in 50 mL?
Step 2: The prefix milli– has a
value of 0.001 of the base unit.
Since L are 1,000 times larger
than mL, the equivalent number
in L will be 1,000 times smaller
than the number in mL. The
decimal will move by three steps.
50 mL =
L
0.05 L is equivalent to 50 mL.
Step 3: The solution is 0.05 L.
(A) 50,000 L
Step 4: Answer choice (D) is
(B) 5 L
correct.
(C) 0.5 L
(D) 0.05 L
Now you try one:
In an experiment, you must measure out 0.13 kg of
sodium chloride. However, your instruments are only
set to work with gram units. Convert 0.13 kg into
grams.
(A) 1.3 g
(B) 13 g
(C) 100 g
(D) 130 g
Explanation
Choice (D) is correct. Since there are 1,000 g in 1 kg, and this is a
conversion to the smaller unit value, simply move the decimal place three
places to the right (once for every 0 in 1,000).
Physics
Learning Objective
In this section, you will learn to:
calculate values for velocity, acceleration, and momentum based
on motion formulas
describe the relation between work, energy, and force
apply Newton’s laws to predict the behavior of physical objects
in different situations
understand visible light as just one part of a spectrum of
different kinds of radiant energy
understand the basic wave behavior of light as it applies to
interactions with mirrors and lenses
understand and identify all instances of heat transference as
either conduction, convection, or radiation
understand the basic origin and behavior of magnetic
phenomena
Physics is the science dealing with the properties, changes, and
interactions of matter and energy. There are many branches of physics,
including mechanics, thermodynamics, magnetism, optics, and electricity.
This review will cover only the physics that might appear on the General
Science section of the ASVAB.
MASS VS. WEIGHT
In physics, words that are o en used imprecisely in everyday
speech have very strict definitions. For example, the words mass
and weight are o en used interchangeably, when in fact they have
very different meanings. Mass is defined as the amount of matter
that something has, whereas weight is defined as the force exerted
on an object’s mass by gravity. A person can become nearly
weightless in deep space, far from the nearest gravity-producing
objects, but that person still has all her mass.
MOTION
Velocity is the rate at which an object changes position. Change in position
is called displacement and velocity is defined as the total displacement
per unit time. It can be calculated as velocity = displacement of an object
÷ time.
In physics, velocity is called a vector quantity, meaning it is fully
described by both a magnitude and a direction. For example, a car
traveling west that covers fi een meters in two seconds would be
described as having a velocity of 7.5 m/s (that is, miles per second) west.
Displacement is also a vector, and both symbols o en have a little arrow
above them to signify this. Time is not a vector.
Momentum is a measure of the quantity of motion of an object. It
corresponds to how difficult it is for a moving object to stop. The formula
definition of momentum is Momentum = mass × velocity. In the symbolic
version, momentum is represented by the letter p, since m is already in use
for mass.
This relationship means, for example, that a semitrailer truck moving at 5
km/h has more momentum than a person walking at the same speed, and
also that you have more momentum when running than when walking.
Momentum is also a vector quantity, so that two objects moving towards
each other have opposite directions of momentum which will partially or
completely cancel out if they collide.
Acceleration is the rate of change of velocity. Acceleration = change in
velocity ÷ change in time. The Δ (delta) symbol represents change.
You can see acceleration in a stopped vehicle when the light turns green
and the driver depresses the gas pedal. The movement of the speedometer
needle shows acceleration, as the car’s velocity is increasing moment by
moment until it plateaus at cruising speed. Acceleration is also a vector
quantity.
Question
Analysis
A sports car hits the brakes and
Step 1: The question asks for the
changes its velocity from 65 m/s
to 40 m/s in five seconds. What is
acceleration of the car. The
change in velocity and time of
its average rate of acceleration?
acceleration are required.
Step 2: Change in velocity is the
difference between the final and
initial velocity. This goes into the
acceleration formula. Velocity
has decreased, so acceleration
should be negative.
Step 3: The acceleration is −5
m/s2, or the car decelerates at a
rate of 5 m/s2. The prediction has
a negative value to denote a
direction opposite motion.
(A) −5 m/s
(B) 5 m/s
(C) 8 m/s
(D) 13 m/s
Now try one on your own.
Step 4: Select choice (A).
A bicycle initially at rest at the top of a hill accelerates
as its rider coasts down. An accelerometer (which
measures acceleration) records a fairly constant
acceleration of 6.5 m/s2. If the rider reaches the
halfway point 5.2 s into the trip, what was the velocity
of the bicycle and rider at this time?
(A) 33.8 m/s, uphill
(B) 1.25 m/s, uphill
(C) 33.8 m/s, downhill
(D) 1.25 m/s, downhill
Explanation
Answer choice (C) is correct. The change in velocity can be calculated by
rearranging the acceleration equation, then written as Δv = at. Since the
bicycle and rider are initially at rest, the change in velocity is equivalent to
the final velocity (a er 5.2 s). This also means that both acceleration and
the velocity any time a er movement has begun are in the downhill
direction. Thus, v2 = (6.5 m/s2)(5.2 s) = 33.8 m/s, downhill.
FORCES AND ENERGY
Force is the push or pull that causes an object to change its speed or
direction of motion.
Weight is just one example of a force; in this case, the force is due to
gravity. A unit of force is called a newton (N), which is the force required to
impart an acceleration of one meter per second squared to a mass of one
kilogram.
Work is performed on an object when there is an applied force that is
along the same line of movement. Work = force × displacement, where
the directions of force and movement are parallel.
A unit of work is called a newton-meter or joule (J). Performing work uses
up energy, also measured in joules, which is equal to the amount of work
performed. The reason we have to regularly consume food is that we are
constantly using up energy: when we move, when our heart pumps blood,
when our lungs inhale and exhale, when we generate warmth to maintain
our body temperature, and so on. The nutritional information on food
packages sometimes lists the food energy per serving in kilojoules (kJ) in
addition to the traditional British unit of kilocalories (usually referred to,
confusingly, as “calories” in everyday speech).
Power is the rate at which work is performed, or energy is converted. It’s
defined as the amount of work done or energy converted per unit of time
and can be calculated as Power = work ÷ time, or Power = (force ×
distance) ÷ time.
The main unit of power is the watt (W), where one watt is defined as one
joule per second. Be sure not to mix up the symbol for the Watt unit with
the symbol for work in the formula, nor the formula symbol for mass with
the symbol for the meter unit. Units go with a number. The letter symbols
in each formula stand for an unknown measurement value which will be
replaced by a number during calculation.
Study this example of an expert approach to an ASVAB question about
measurement in science.
Question
Analysis
Once outside the Earth’s
Step 1: The question asks for the
atmosphere, a space shuttle’s
propulsion system effects a net
force of 10,000 N over a distance
increase in energy. Because
energy and work are both
measured in joules, the answer
of 50 m. The potential energy of
the cra is unchanged during this
time. What increase in kinetic
will be in joules.
energy will result?
Step 2: Since work performed
results in a conversion of energy
from one form to another, the
amount of increased kinetic
energy (energy of movement) has
to be the same as the amount of
work done.
The formula for work is known.
Question
Analysis
Step 3: The increase in kinetic
energy will be equal to the
amount of work done, or 500,000
J.
(A) 0 J
Step 4: Select choice (D).
(B) 0.005 J
(C) 200 J
(D) 500,000 J
Now you try your hand at a question.
A hydroelectric dam captures the energy of falling
water in order to provide electrical power to the grid.
The water turns a turbine a total distance of 2.5 m
every 10 s. The average force the water applies to the
turbine is 10,000 N. What is the average rate of
hydroelectric power generation of that turbine?
(A) 25 W
(B) 2,500 W
(C) 25,000 W
(D) 250,000 W
Explanation
Choice (B) is correct. The work done by the falling water is equal to
W = 10,000 N × 2.5 m = 25,000 J
Power is the rate at which work is done, or at which energy is used,
converted, or delivered.
P = 25,000 J / 10 s = 2,500 W
NEWTON’S LAWS
Sir Isaac Newton was an English mathematician and physicist. In the
seventeenth century, he came up with some of our most important
formulas for understanding the properties of motion and gravity.
Newton’s first law of motion. An object at rest tends to stay at rest, and an
object in motion tends to stay in motion at a constant speed in a straight line
(constant velocity), unless acted upon by an unbalanced force. An example
of an unbalanced force—one that keeps objects in motion from staying in
motion on Earth—is friction, the force that resists relative motion between
two bodies in contact. This law is also known as the law of inertia, with
inertia referring to the tendency of all matter to resist changes in its
motion.
Newton’s second law of motion. When dealing with an object for which all
existing forces are not balanced, the acceleration of that object, as produced
by the net force, is in the same direction as the net force and directly
proportional to the magnitude of the net force, and is inversely proportional
to the object’s mass. Expressed mathematically, acceleration = net force ÷
mass. When using this formula, the units for each of these measures must
be m/s2, N, and kg, respectively.
The greater the mass of an object, the greater the force needed to
overcome its inertia. This law actually encompasses the first law, as the
special case of zero net force results in zero acceleration, i.e., no change in
motion. Sometimes this law is written in the equivalent form, net force =
mass × acceleration.
Newton’s third law of motion. For every action, there is an equal and
opposite reaction. In other words, when an object exerts a force on another
object, the second object exerts a force of the same magnitude but in the
opposite direction on the first object. For example, consider what happens
when a gun is fired. A bullet fires and the gun recoils. The recoil is the result
of action-reaction force pairs. As the gases from the gunpowder explosion
expand, the gun pushes the bullet forward and the bullet pushes the gun
backward. The acceleration of the recoiling gun is, however, smaller than
the acceleration of the bullet, because acceleration is inversely
proportional to mass, and the bullet, as a rule, has a smaller mass than the
gun, and is more easily accelerated.
In addition to those three laws of motion, Newton also developed
Newton’s law of universal gravitation. All objects in the universe attract
each other with an equal force that varies directly as a product of their
masses, and inversely as a square of their distance from each other. This
force is known as gravity. Newton’s law of universal gravitation is expressed
by the following equation (where G is a constant with a value of 6.67 × 10−11
and r is the distance between the two objects’ centers of mass):
Take, for example, the gravitational force between the Sun and the Earth.
The following consequences follow from the law of universal gravitation:
If the mass of the Earth were doubled, the force on the Earth would
double.
If the mass of the Sun were doubled, the force on the Earth would
double.
If the Earth were twice as far away from the Sun, the force on the Earth
would be a factor of four smaller.
The force exerted on the Earth by the Sun is equal and opposite to the
force exerted on the Sun by the Earth (Newton’s third law).
At the surface of the Earth, the acceleration due to gravity is 9.8 m/s2. This
bears remembering, and can be applied to the formula for Newton’s
second law to determine the weight (gravitational force) of any object
given its mass.
Question
Analysis
Question
Analysis
A 600 g squid propels itself by
firing a jet of water with a force of
Step 1: The question asks for
acceleration and provides mass
21 N. The water jet is pointed in
an easterly direction. What will
and force, which means Newton’s
laws are being used.
be the acceleration of the squid?
Step 2: The squid is firing a jet
towards the east; however, the
question asks about the
acceleration of the squid, not the
water jet. From Newton’s third
law, the water being pushed out
in a jet to the east is
simultaneously pushing on the
squid to the west with the same
force, which means acceleration
will be westward.
The mass of the squid must be
converted to kg, and then, along
with the given force, used to find
magnitude of acceleration.
Force on squid (equal and
opposite) = 21 N, west
Mass of squid =
a=
= 35 m/s2, west
kg
Question
Analysis
Step 3: Acceleration is 35 m/s2,
west. Both the calculated
magnitude and the reasoned
direction must be included in the
prediction.
(A) 0.035 m/s2, west
Step 4: Choice (C) matches the
(B) 35 m/s2, east
(C) 35 m/s2, west
prediction.
(D) 28.6 m/s2, east
Now try one on your own:
A man pushes a 15 kg shopping cart across a rough
surface, applying a force of 15 N in the direction of
motion. A friction force resists the movement of the
wheels across the surface with a magnitude of 15 N
opposite to the direction of motion. What will be the
effect on the motion of the shopping cart?
(A)
(B)
(C)
(D)
The
The
The
The
Explanation
cart
cart
cart
cart
will
will
will
will
slow down at a rate of 1 m/s2.
continue its uniform velocity.
speed up at a rate of 1 m/s2.
speed up at a rate of 2 m/s2.
The correct answer is (B). Since the two forces acting on the cart are equal
in magnitude but opposite in sign (direction), the net force will be equal to
zero. Net force = +15 N − 15 N = 0 N. By Newton’s second law, with no net
force there can be no acceleration, which means, by definition, the velocity
will not change.
ENERGY
As mentioned earlier in this chapter, energy can be defined as the
capacity to do work. Many ASVAB energy questions deal with mechanical
energy, which may be either kinetic or potential. Kinetic energy is the
energy possessed by a moving object. Potential energy is the energy
stored in an object as a result of its position, shape, or state.
According to the law of conservation of energy, energy can neither be
created nor destroyed. Instead, it changes from one form to another. For
example, if a rock is poised right at the edge of a cliff, the rock has potential
energy relative to the ground at the bottom of the cliff. If the rock is
dislodged and falls freely, that potential energy is converted completely to
kinetic energy at the instant just before the rock hits the ground.
Sound and light energy travel in waves (although it gets complicated in the
case of light). So let’s take a look at the properties of waves.
SOUND WAVES
Sound waves are produced when an object vibrates, disturbing the
medium around it, creating an outward ripple in all directions. These
ripples (waves) can travel through air, liquids, and solids, but they cannot
be transmitted through a vacuum, or empty space. Sound waves
transmitted through air do not travel as fast as those transmitted through
water, and those transmitted through water do not travel as fast as those
transmitted through metal or wood.
The pitch of sound is directly related to the frequency (rate of vibration) of
the sound waves. Sound waves with a high frequency (high rate of
vibration) produce a high pitch. Frequency is usually measured in hertz
(Hz), defined as the number of repetitions per second. Sound waves with a
very high pitch (high number of vibrations per second) are inaudible to
humans, although they can be heard by dogs and other creatures. The
typical audible hearing range for a human is from about 20 Hz to 20 kHz.
Sometimes, a human (or a dog, for that matter) will perceive a sound as
being a different frequency than the actual frequency of the sound. This is
due to the Doppler effect. The Doppler effect occurs when either the
source of the sound waves, the listener, or both, are moving closer together
(pitch frequency sounds higher than it is) or farther apart (pitch frequency
sounds lower than it is). A perfect example of the Doppler effect is the way
the sound of a police or ambulance siren seems to change when it zooms
by.
THE ELECTROMAGNETIC SPECTRUM
It’s important to realize that visible light makes up only one small part—the
visible part—of the electromagnetic spectrum. The electromagnetic
spectrum covers all the different wavelengths and frequencies of
radiation. Visible light waves fall in the middle of the electromagnetic
spectrum. Starting with lowest frequency (which corresponds to the
longest wavelength), the electromagnetic spectrum goes from radio
waves to microwaves to infrared waves to visible light to ultraviolet
light to X-rays and finally to gamma rays, the most active radiant energy
known to exist.
Visible light breaks down into different colors as well, based upon the
frequency of the waves. Red has the lowest frequency, which is why
wavelengths just below the frequency of visible light are called infrared;
likewise, violet has the highest frequency, so wavelengths just above the
frequency of visible light are called ultraviolet.
OPTICS
As noted above, light, as well as the entire
electromagnetic spectrum, possesses properties of waves. However, unlike
sound waves, which are mechanical, light waves are electromagnetic and
can travel through empty space. They also travel at much higher speeds
than do sound waves. The speed of light in a vacuum is 299,792,458 meters
per second (or roughly 300 million meters per second or 186,000 miles per
second).
Refraction
It should be noted, however, that the effective speed of light can vary
depending on the material the light waves are passing through; for
example, light passes more slowly through water or glass than through a
vacuum. The ratio by which light is slowed down is called the refractive
index of that medium. For instance, the refractive index of a diamond is
2.4, which means that light travels 2.4 times faster when passing through a
vacuum than when traveling through a diamond.
The change in speeds causes light to bend when passing from one medium
to another (like a vehicle changing direction when hitting a slick patch of
road). This bending is what’s called refraction, and light bends at a greater
angle when the change in the index of refraction is greater.
Reflection
Any wave, including light, that bounces off a flat, smooth barrier follows
the law of reflection, which states that the angle of incidence is equal to
the angle of reflection as measured from a line normal (at a 90° angle) to
the barrier. In the case of light, this barrier is o en a mirror.
The Law of Reflection
Concave and Convex Mirrors and Lenses
Mirrors and lenses either can be flat, or they can be concave (curved in, like
a cave) or convex (curved out, like a swelling). Because of the law of
reflection, a concave mirror is also called a converging mirror, because
the angles of incidence of rays of light parallel to the normal all converge
upon a point.
Converging Mirror
If you draw the mirror away from the source of the image, the image falls
out of focus as the image source nears the mirror’s focal point, the point
where the mirror’s angles of incidence converge. As the image source
keeps moving beyond the focal point, the image reappears in the mirror,
only upside down.
A convex mirror, on the other hand, is known as a diverging mirror
because it diverges the light waves that strike it.
Lenses, unlike mirrors, operate on the principle of refraction. A convex
lens—one that is thicker in the middle than on the edges—is also called a
converging lens because it converges parallel waves that pass through it.
This type of lens is used in reading glasses to correct farsightedness, as
well as in magnifying glasses, cameras, telescopes, and microscopes.
A concave lens—one that is thicker on the edges than it is in the middle—is
also known as a diverging lens because it diverges the light waves that
pass through it. In nearsightedness, light waves converge before they meet
the retina. A nearsighted person sees objects close up but not far away. A
concave lens placed before the eye bends light so that it converges further
back in the eye, reaching the retina and correcting nearsightedness.
Converging Lens (a) and Diverging Lens (b)
Study the approach an expert test taker would use on an ASVAB question
about optics.
Question
Analysis
Through which medium will light
travel the fastest?
Step 1: The question asks for the
fastest medium for light to travel
through.
Step 2: Light is slowed down by
different materials. Materials with
high indices of refraction tend to
be denser, and slow down light
the most. The least dense
material should provide light the
greatest speed.
Step 3: The answer choice with
the least dense material will be
correct.
Question
Analysis
(A) a vacuum
(B) air
Step 4: Of the available choices,
empty space, or (A) a vacuum, is
(C) diamond
(D) pure hydrogen
the least dense material (or lack
of material) possible. Light
should travel fastest through a
vacuum. In fact, the “speed of
light” is defined for a vacuum.
Try your hand at the question below.
“Waves” of heat can be seen above a hot stove element
or flame, as the background appears to be distorted or
out of focus just at that spot. This is an example of
(A) diffraction
(B) refraction
(C) reflection
(D) convergence
Explanation
Choice (B) is correct. The background can only appear distorted if the light
rays are following a different path through the heated area than other light
rays moving through the room. Since the light is still traveling through the
space, rather than being bounced away, this is refraction, not reflection. It
occurs because the air near the heat source is of a different density,
resulting in different indices of refraction in different patches of air.
HEAT
There are three means by which heat energy may be transferred from one
object to another: conduction, convection, and radiation. Heat energy is
always transferred from warmer to cooler environments.
Conduction is the simplest method of heat transfer. It is accomplished by
direct contact, such as placing your finger on a hot iron, which we
recommend that you not try at home. Metals are generally good
conductors of heat. Other materials, such as wood, Styrofoam, and plastic,
are poor conductors of heat, which makes them good insulators.
Convection transfers heat by the actual movement of hot particles of a
fluid. The hot air rising from a bonfire is an example of convection. Ocean
currents and wind are caused by convection movements caused by
temperature differences.
Radiation occurs when electromagnetic waves transmit heat. The heat we
get from the Sun travels through space as radiation.
MAGNETISM
Simple magnets have two poles: a north pole and a south pole. Much as it
happens in a Hollywood romance, opposites attract. If you try to bring
together two north poles of a magnet—or two south poles, for that matter
—they will repel one another, and you can feel their repulsive force. If, on
the other hand, you move the north pole of one magnet toward the south
pole of another magnet, they will attract each other.
Because the Earth itself is magnetized and has a North Pole and a South
Pole, a magnetic compass, which contains a small, lightweight magnet
balanced on a nearly frictionless, nonmagnetic surface, can be used to tell
direction. The magnet, which is generally called a needle, has one end
marked with an arrow and o en the letter “N.” This end of the needle is the
magnet’s south pole, which constantly orients itself to point toward the
Earth’s North Pole, allowing the person reading the compass to gain
bearings from that direction.
Study the example below.
Question
The arrival of a warm front, a
mass of hot air moving into an
area, is an example of
Analysis
Step 1: The question asks for a
phenomenon to be identified as
one of three methods of heat
transfer or as a magnetic effect.
Step 2: The methods of heat
transfer are identified by how
heat energy physically travels. If
actual hot physical molecules
bring heat with them, it’s
convection.
Question
Analysis
Step 3: The question stem
specifies that the warm air itself
is moving into the area. By
definition, that makes this an
example of convection.
(A) conduction
(B) convection
Step 4: Choice (B) matches the
prediction.
(C) radiation
(D) the Earth’s magnetic field at
work
Now you try one:
Wooden spoons are sometimes used in kitchens
instead of metal ones when stirring hot pots of soup.
What’s a reasonable explanation for this?
(A) Wood does not conduct heat as well as metal, so
the person stirring won’t get burned.
(B) Wood draws in convection heat so that it does not
flow into the pot.
(C) Wood is magnetic and diverts heat.
(D) Wood is a good conductor of radiation.
Explanation
Choice (A) is correct. Of the methods of heat transfer, only conduction
would allow heat to move from a hot liquid into a solid spoon. It makes
sense that a less conductive material would be purposely chosen to
minimize the amount of heat that is able to travel from the soup, through
the spoon, to the cook’s fingers. The other choices, on the other hand,
suggest a misunderstanding of how the methods of heat transfer work.
Chemistry
Learning Objective
In this section, you will learn to:
understand what differentiates one element from another
find information using the periodic table
differentiate compound substances from pure elements, and
understand the ways in which they are built up from simpler
elements and/or compounds
understand the basic definitions of acids and bases and their
relation to the pH scale
describe phase transitions and the defining features of the solid,
liquid, and gaseous states of matter
understand the basic definition and process of a chemical
reaction, and differentiate this from physical change
ELEMENTS AND THE PERIODIC TABLE
Chemistry is the science dealing with the composition and properties of
matter, and with the reactions by which matter is produced from or
converted into other types of matter. Matter is anything that has mass and
occupies space, and any form of matter has certain chemical properties
based upon its molecular composition. To start, here are some basic terms:
Element: A pure type of matter that cannot be separated into different
types of matter by ordinary chemical methods. All matter is composed
of elements, and all the known elements are listed on the Periodic Table
of Elements (see the figure on the next page).
Atom: The smallest component of an element that still retains the
properties of the element. An atom may combine with similar particles
of other elements to produce compounds. Atoms consist of a complex
arrangement of electrons in motion about a positively charged nucleus
containing protons and (except for hydrogen) neutrons.
Proton: A subatomic particle found in the atom’s nucleus that carries a
positive electric charge.
Neutron: A subatomic particle found in the atom’s nucleus that does not
have an electric charge and is therefore neutral.
Electron: A subatomic particle that orbits the nucleus of an atom. An
electron carries a negative charge and has a miniscule mass compared
to the other subatomic particles (both neutrons and protons are more
than 1,800 times as massive as an electron). Ordinarily, an atom has the
same number of negative electrons around the nucleus as the number
of positive protons in the nucleus.
Structure of an Atom
Molecule: The smallest multi-atom particle of an element or compound
that can exist in the free state and still retain the characteristics of the
element or compound. The molecules of elements consist of two or
more similar atoms; the molecules of compounds consist of two or more
different atoms.
Through decades of research, scientists have organized all the known
elements into a structure called the periodic table, which conveys multiple
pieces of information about each element.
Periodic Table of Elements
In order to be able to read the Periodic Table of the Elements, there are a
few things you need to understand. For starters, elements are arranged in
order of increasing atomic number, from le to right and from top to
bottom. An element’s atomic number represents the number of its protons
(and also the number of its electrons, since those two numbers are the
same). The different rows of elements are called periods. The periods
correspond to the shells, or the different orbits that electrons occupy
around atoms. As a rule, electrons will occupy the lowest shell they can,
and move on to higher shells only a er lower shells are occupied (although
this rule is sometimes violated) so as to minimize the energy of the atom.
Every element in the top row (the first period) has one shell for its
electrons. Every element in the second row (the second period) has two
shells for its electrons, and so on. At this time, the maximum number of
shells is seven.
The Periodic Table has a special name for its columns, too. The elements in
a column are called a group. The elements in a group have the same
number of electrons in their outer shell. It is the group that an element
occupies, much more than the period, that determines its chemical
properties. This is because the number of electrons needed to complete an
element’s outer shell shapes the way in which it reacts with other elements
to form molecules. For instance, every element in the first column (Group I)
has one electron in its outer shell. The elements in this group are called
alkali metals, which describe so , silvery metals that react strongly with
water. The further down the group you go, the more violent this reaction is.
By the same token, every element on the second column (Group II) has two
electrons in the outer shell. As you keep counting the columns, you’ll know
how many electrons are in the outer shell. Note that the far right-hand
column is composed of a group called the noble gases, sometimes
referred to as inert gases, because these elements generally don’t react
with other elements since their outer shell is completely filled.
Atomic Structure of Lithium and Sodium
Notice that Li has two electron shells, so it is in the second row of the
periodic table; Na has three shells, so it is in the third row. Both elements
have one electron in their outer shell and are, therefore, in Group I.
Besides these important chemical properties, an element’s atomic mass is
also related to its position on the Periodic Table. The atomic mass listed in
an element box represents the average mass of a single atom. Why
average? Because some elements can vary in their number of neutrons, so
individual atoms of an element may be found in a couple of slightly
different sizes. These different sizes are referred to as isotopes.
A pretty good estimate of atomic mass comes from adding the total
number of neutrons and protons together. Each proton and neutron has a
mass very close to what’s called an atomic mass unit (amu). The majority
of hydrogen atoms have only one proton, so its atomic mass should be
very close to one, and is, at 1.007 amu.
Now take a look at an individual element box within the Periodic Table.
Here’s chlorine.
Chlorine
Chlorine’s atomic number is 17, which is the number of protons in the
nucleus of a chlorine atom and also the number of electrons orbiting its
shells. Its atomic symbol, Cl, is fairly close to its name, unlike the symbols
of some other common elements, such as Fe (iron), Au (gold), Ag (silver), W
(tungsten), or Na (sodium), symbols that derive from the elements’ Latin
names, rather than their familiar English names.
Finally, the atomic mass of chlorine is listed as 35.5, due to about half of
chlorine atoms being close to 35 amu and the other half closer to 36 amu.
Since all chlorine atoms have 17 protons, this means chlorine atoms are
almost as likely to have either 18 or 19 neutrons.
Question
Analysis
How many neutrons does a
Step 1: The question asks for the
single sulfur (S)
number of neutrons in sulfur,
atom have?
which are found in the nucleus of
an atom with the protons.
Question
Analysis
Step 2: Since the atomic mass is
about equal to the total number
of protons and neutrons, and the
atomic number is defined by the
number of protons, the difference
in these values (available on the
Periodic Table earlier in this
section) should be about equal to
the number of neutrons. Round
the atomic mass to the nearest
whole number as necessary.
For sulfur:
Atomic # (protons) = 16
Atomic mass = 32.1
Number of protons and neutrons
= 32
Number of neutrons = 32 − 16 =
16
Step 3: It isn’t possible for an
atom to have something other
than a whole number of
neutrons, so round to the nearest
whole number. There are exactly
16 neutrons.
Question
Analysis
(A) 16
(B) 16.1
(C) 32
Step 4: Select choice (A).
(D) 48
Now try one on your own:
How many protons, neutrons, and electrons do argon
(Ar) atoms have?
(A) 18, 18, 18
(B) 18, 22, 18
(C) 18, 21.9, 18
(D) 18, 22, 22
Explanation
Answer choice (B) is correct. Argon’s atomic mass is about 40, so there are
18 protons and 22 neutrons, and, in neutral atoms, there are always the
same number of electrons as protons.
COMPOUNDS
Unstable elements readily form into compounds with properties very
distinct from the elements from which they are composed. For instance,
sodium and chlorine, both of which are extremely unstable and noxious as
elements, combine to form the stable and edible compound sodium
chloride (NaCl), more commonly known as table salt. Table salt is called an
ionic compound because each chlorine atom borrows an electron from
each sodium atom and the atoms stick closely together to form a very
tightly bound crystalline structure when salt is in solid form. When it is
placed in solution, however, such as when table salt is poured in water, the
atoms dissociate into sodium ions and chloride ions. An ion is an
electrically charged atom; in this case, each of the sodium atoms is
positively charged because it has lent an electron to its corresponding
chloride atom, and each of the chloride atoms is negatively charged for the
same reason.
Table sugar is an example of a covalent compound, which means, among
other things, that it does not ionize when dissolved in water. In a covalent
compound, the atoms in the molecule have covalent bonds; that is, they
share electrons in pairs, so that each atom provides half the electrons, and
the pair is held tightly by both atoms. For this reason, they will not separate
as ions do.
ACIDS AND BASES
An acid is a substance that gives up positively charged hydrogen ions (H+)
when dissolved in water. Acids corrode metals and generally have a sour
taste (though not all acids are safe to drink). Some common acidic
solutions are vinegar (which has acetic acid) and lemon juice (which has
citric acid). More potent acids include hydrochloric acid, nitric acid, and
sulfuric acid (commonly used in lead batteries), all of which are extremely
corrosive and must be handled with the utmost care.
A base is a substance that gives up negatively charged –) hydroxyl ions
(OH-) when dissolved in water. Basic substances are also referred to as
alkaline. Bases typically taste bitter.
Some common basic substances found in a kitchen include baking soda
(sodium bicarbonate) and liquid soap (which o en includes potassium
hydroxide). More potent bases include sodium hydroxide (also known as
lye) and sodium hypochlorite (the most common active ingredient in
bleach), and these are just as corrosive and dangerous as comparable
acids. When acids and bases react (and they react together rather
powerfully), the substances neutralize each other and turn into water and a
salt.
The pH of a solution is a number from 0 to 14 that indicates how basic or
acidic that solution is. According to the pH scale, solutions with a pH less
than 7 are acidic, with the degree of acidity increasing tenfold with each
declining number. For instance, black coffee has a pH of 5; vinegar, which is
100 times as acidic as coffee, has a pH of 3; and battery acid, which is 100
times as acidic as vinegar, has a pH of 1. A solution with a pH of 7 is neutral.
Pure water has a pH of 7.
Common Substances on the pH Scale
Solutions with a pH greater than 7 are basic, with the degree of alkalinity
once again increasing tenfold with each increasing number. Baking soda
has a pH that is a little over 8. Borax, commonly used in cleaning solutions
and detergents, is about 10 times as basic, at just over 9 on the pH scale,
while household bleach, over 12 pH, is 1,000 times as basic as borax, and
10,000 times as basic as baking soda. Human blood, just above pH 7, is just
slightly basic, with about one-tenth the alkalinity of baking soda.
Study this example of an expert test taker’s approach to a question about
acids and bases.
Question
Analysis
In a chemistry lab, you are given
four solutions and measure their
Step 1: The question asks for the
highest concentration of
pH values. Which solution
contains the greatest number of
hydrogen ions.
hydrogen ions?
Step 2: Acids produce hydrogen
ions, and more acidic substances
produce them in greater
concentrations. Lower pH values
indicate more acidic substances,
which means the most
hydrogen ions.
(A) the pH 2.5 solution
Step 4: Answer choice (A) has the
(B) the pH 3.7 solution
(C) the pH 7.1 solution
(D) the pH 9 solution
lowest pH.
Now try your hand at a question about acids and bases.
You find a mystery substance in the lab and note the
following qualities: it’s bitter to the taste, it releases
OH– ions in solution, and it reacts with an acid to form
a salt and water. Which of the following could the
mystery substance be?
(A) vinegar
(B) soap
(C) lemon juice
(D) water
Explanation
Choice (B) is correct. The properties of the mystery substance match those
of a base. Of the choices given, the only basic substance is soap.
PHYSICAL CHANGE
Matter may undergo either a physical change or a chemical change. The
form, size, and shape of matter may be altered in a physical change, but
the molecules remain unchanged. Building a sand castle or bending a
piece of plastic into a new shape are both physical changes. The matter has
been rearranged, but it is still made of up of the same kinds of atoms and
molecules. In other words, its chemical identity has remained intact.
One of the most important kinds of physical change is what’s known as a
phase transition. A phase transition is when matter switches from one
state of matter, like solid, liquid, or gas, to another.
The solid state exists at lower temperatures relative to the liquid and
gaseous states (although the specific temperature ranges depend on the
element or compound). In the solid state, atoms or molecules are packed
very close together and do not move freely. Solids maintain a constant
volume and shape. A good example is an ice cube, consisting of solid-state
water molecules.
The liquid state exists at a higher temperature range relative to the solid
state equivalent of the same element or compound. In the liquid state,
molecules flow freely around each other. Liquids have a constant volume,
but do not maintain their shape. They will either take on the shape of their
container or, let free, will spread out into a puddle. Water from a faucet
comes out in the liquid state.
The gaseous state occurs at a higher temperature range relative to the
previous two states of matter. In the gaseous state, molecules flow even
more freely from each other, and will also spread out as far as they can.
Gases do not maintain either a constant volume or shape. A small amount
of gas will spread to fill a large volume if space is available, or can be highly
compressed into smaller spaces (oxygen tanks include a large amount of
compressed oxygen gas). Steam or vapor are the common terms for water
in a gas state.
Under certain circumstances, it’s possible for solids and gases to transition
between each other directly, without transforming to the liquid state first.
The specific terms for each type of phase transition are summarized below.
Phase Changes
CHEMICAL CHANGE
In a chemical change, molecules of new matter are formed that are
different from the original molecules of matter. When elements and
compounds undergo a chemical change, the process is called a chemical
reaction. During a chemical reaction, atoms are rearranged into new
combinations, resulting in different kinds of molecules. The molecules and
atoms that enter the reaction are called reactants and the molecules and
atoms that result from the reaction are called products.
For example, water is also known as H2O because a single water molecule
is made of two hydrogen atoms and one oxygen atom. One kind of
chemical reaction will cause many water molecules to break apart and the
atoms to rearrange into hydrogen molecules (H2) and oxygen molecules
(O2). This is how the reactant, water, is turned into the products, pure
hydrogen gas and oxygen gas. Other common examples of chemical
reactions include the formation of rust on iron, and the conversion of wood
into charcoal, carbon dioxide, and steam in a fire.
To illustrate the profound effects of chemical change, consider one more
example: the reaction of chlorine gas and sodium metal. Both substances,
in their pure forms, are extremely hazardous to humans. Sodium metal
cannot be touched with bare hands; it reacts with any moisture, giving off
heat and sparks. It’s stored in oil when not in use. Chlorine gas was used as
a devastating chemical weapon in the First World War. Yet, these two
dangerous substances can undergo a chemical reaction that results in a
product of sodium chloride: common table salt, found in any kitchen.
That’s the power of chemical change.
Here’s how the well-prepared test taker would approach a question about
states of matter.
Question
Analysis
A sample of matter with an
Step 1: The question asks for the
amorphous shape but constant
volume has to be
type or phase of matter with a
constant volume but non-fixed
shape.
Step 2: A solid has a fixed shape.
A liquid will take the shape of its
container, or more exactly, find
the lowest possible level.
Step 3: The only thing that
logically must be true of the
matter sample based on the
qualities described in the
question is that the substance
must be in the liquid phase.
Question
(A) in the solid phase
(B) in the liquid phase
(C) a pure element
(D) a compound
Analysis
Step 4: Select choice (B). (Note
that the sample could be either
an element or a compound, since
both elements and compounds
are capable of being solid, liquid,
or gas. Thus, neither (C) nor (D)
has to be true.)
Now try one on your own.
Energy is needed for which of the following changes of
state?
(A) solid to liquid
(B) gas to liquid
(C) liquid to solid
(D) gas to solid
Explanation
Choice (A) is correct. Liquids occur at higher temperatures than solids, and
gases occur at higher temperatures still. The melting of a solid into a liquid
is the only answer choice listed that involves movement to a phase that
occurs at higher temperatures, requiring a net input of energy to allow the
molecules the freer movement that occurs in the liquid phase.
Physical Science Practice Questions
1. What is 77°F in degrees Celsius?
(A)
(B)
(C)
(D)
25°C
32°C
37°C
5°C
2. Which of the following best explains the recoil action of a shooting
gun?
(A)
(B)
(C)
(D)
Newton’s first law of motion
Newton’s second law of motion
Newton’s third law of motion
Newton’s law of universal gravitation
3. The weight of a pendulum clock transforms potential energy to
usable mechanical work. Assuming no energy loss, approximately
how much work will be done if a 200 g weight descends 0.5 m?
(A)
(B)
(C)
(D)
0.1 J
1J
100 J
1000 J
4. Which of the following waves on the electromagnetic spectrum has
the highest frequency?
(A)
(B)
(C)
(D)
microwaves
X-rays
visible light
radio waves
5. Pure water has a pH of
(A) 1
(B) 7
(C) 0
(D) 14
6. During a game of baseball, two players both attempt to catch the
same ball. The 50 kg Player A is traveling west at 12 m/s, while the
60 kg Player B is traveling east along the same line at 10 m/s. What
will happen when they collide?
(A) Player A will continue forward at reduced velocity, knocking
back Player B.
(B) Player B will continue forward at reduced velocity, knocking
back Player A.
(C) Player B will continue forward without any decrease in
velocity, knocking back Player A.
(D) Player A and Player B will both come to a complete stop.
7. A truck was driven
meters. At the beginning of the
trip, the fuel tank contained 40,000 mL of fuel; at the end of the trip,
it still had 15,000 mL of fuel. What was the average fuel
consumption, measured in liters per kilometer, for the trip?
(A) 0.0125 L/km
(B) 0.125 L/km
(C) 8.0 L/km
(D) 80 L/km
8. The apparent sound of a train's horn changes from a higher to a
lower pitch as the train approaches and then passes a stationary
observer. This phenomenon is called
(A) a Newtonian shi
(B) sound wave compression
(C) the Doppler effect
(D) an auditory aberration
9. If an object is viewed through a converging lens, when will the
object appear to be upside down?
(A) always
(B) never
(C) when the observer is closer to the lens than the focal length
(D) when the observer is farther from the lens than the focal
length
10. If a block of solid frozen carbon dioxide ("dry ice") is le in a
container that is open to the air, some frozen carbon dioxide will
become carbon dioxide gas without becoming a liquid first. This
phase change is called __________.
(A) sublimation
(B) evaporation
(C) vaporization
(D) gasification
Answers and Explanations
PHYSICAL SCIENCE PRACTICE QUESTIONS
1. A
To convert the temperature from degrees Fahrenheit to degrees
Celsius, first subtract 32, and then multiply by .
2. C
The recoil action of a shooting gun is explained by Newton’s third law
of motion: for every action, there is an equal and opposite reaction.
3. B
Using Newton’s second law, and the fact that acceleration near the
surface of the Earth is 9.8 m/s2, the force of gravity can be calculated.
The mass must be converted to kg units first: m = 200 g = 0.2 kg. Then
the force is (0.2 kg) × (9.8 m/s2) = 1.96 N. This force acts over a distance
of 0.5 m, so W = (1.96 N) × (0.5 m) = .98 J. Answer choice (B) is the
closest match.
4. B
Of the wave states listed, X-rays have the highest frequency in the
electromagnetic spectrum (gamma rays have an even higher
frequency).
5. B
Pure water has a pH of 7, making it a neutral solution.
6. D
Determine each player's momentum. Player A has a momentum of 50
kg × 12 m/s = 600 kg·m/s in a westward direction. Player B has a
momentum of 60 kg × 10 m/s = 600 kg·m/s in an eastward direction.
Since the two players’ momentums are equal in magnitude but
opposite in direction, the total momentum is zero (Ptotal = (+600) +
(−600) = 0 kg·m/s). To put it another way, since neither player has a
greater quantity of motion than the other, neither one can “win” in a
collision. If neither is able to overcome the other, both coming to a
stop is the only option that makes sense.
7. B
First convert the quantities given to the units of measurement of the
answer. Since kilo– is the prefix for 1,000, the truck traveled
kilometers (km). The
amount of fuel consumed was 40,000 – 15,000 = 25,000 mL. The prefix
milli– means one thousandth, so that converts to 25 liters (L). Since the
desired units are liters/kilometer, divide 25 L by 200 km to get 0.125
L/km.
8. C
This is a classic example of the Doppler effect, which is caused by the
relative motion of a sound source and receptor.
9. D
Light waves converge at a distance equal to the focal length of a lens.
Beyond that distance, the waves from the top of the observed object
are below those from the bottom of the object, making the object
appear to be inverted.
10. A
When a liquid changes to a gas, that process is evaporation under
natural conditions and vaporization if heat is applied. The
transformation directly from solid to gas is called sublimation.
Part IV
GENERAL SCIENCE PRACTICE
QUESTIONS
GENERAL SCIENCE PRACTICE SET 1
Choose the best answer for each multiple-choice question. This
question set has 15 practice questions, which is the number of
General Science questions you will see if you take the CAT-ASVAB.
1. Which of the following best describes the difference between
eukaryotic cells and prokaryotic cells?
(A) Prokaryotic cells do not have nuclei.
(B) Prokaryotic cells are only found in plants.
(C) Eukaryotic cells are only found in plants.
(D) Eukaryotic cells do not have nuclei.
2. Which of the following is a terrestrial planet?
(A)
(B)
(C)
(D)
Mars
Jupiter
Saturn
Neptune
3. When a skydiver jumps from a plane, she eventually reaches a
maximum falling velocity of −56 m/s. A er opening up her
parachute, her falling velocity decreases to about −11 m/s. What
effect on her motion does the skydiver’s parachute have?
(A) The parachute does not change the skydiver’s velocity.
(B) The parachute applies a negative acceleration on the
skydiver.
(C) The parachute applies a positive acceleration on the skydiver.
(D) The parachute applies first a negative acceleration, then a
positive acceleration on the skydiver.
4. A freight elevator is used to li loads of 12,000 N a vertical
distance of 250 m. The elevator takes 10 s to make this trip.
Assuming no energy loss, what is the average power expenditure
of the elevator, when working?
(A) 300,000 W
(B) 3,000,000 W
(C) 12,000,000 W
(D) 30,000,000 W
5. The air in the troposphere is made up primarily of
(A) oxygen
(B) helium
(C) carbon dioxide
(D) nitrogen
6. The cell membrane that surrounds an animal cell is a
(A) non-permeable structure
(B) semi-permeable structure
(C) fully permeable structure
(D) cell wall
7. In which level of the atmosphere does all weather take place?
(A) troposphere
(B) stratosphere
(C) mesosphere
(D) thermosphere
8. Which of the following is NOT true about the element hydrogen
(H)?
(A) It is the only element with no neutrons.
(B) It is the lightest element.
(C) It is a noble (inert) gas and rarely reacts.
(D) It sometimes behaves like an alkali metal.
9. Which of the following activities results in a chemical change?
(A) mixing salt and sugar
(B) drying wet clothes
(C) boiling a pot of water
(D) burning pieces of wood
10. Air flow in the stratosphere is primarily
(A) horizontal
(B) vertical
(C) clockwise
(D) counterclockwise
11. Iron is a mineral that is vital to red blood cell development. Foods
that are good sources of iron include __________.
(A) meats, beans, and whole grains
(B) nuts and green leafy vegetables
(C) bananas, sweet potatoes, nuts, and seeds
(D) milk, yogurt, cheese, and spinach
12. If a pencil is placed in a clear glass of water and viewed from the
side, the pencil will appear to bend sharply at the top of the water.
This is due to a phenomenon known as __________.
(A) elusivity
(B) reflection
(C) refraction
(D) rotation
13. Red blood cells are produced in ___________.
(A) the liver
(B) kidneys
(C) bones
(D) the spleen
14. Which of the following is NOT an example of phase change?
(A) fuel burning in a
combustion engine
(B) dry ice changing directly from a solid to a gas
(C) sleet melting on a sidewalk
(D) morning dew appearing on a lawn
15. HIV (human immunodeficiency virus) is transmitted __________.
(A) by touch
(B) through the air
(C) by bodily fluids
(D) by proximity to an infected person
GENERAL SCIENCE PRACTICE SET 2
Choose the best answer for each multiple-choice question. This
question set has 15 practice questions, which is the number of
General Science questions you will see if you take the CAT-ASVAB.
16. The Earth experiences seasonal patterns of weather because
__________.
(A) its distance from the Sun varies at different times of the year
(B) solar wind activity varies
(C) its orientation to the Sun is tilted on its axis
(D) the Moon's position relative to the Earth varies
17. Body functions such as heart rate and digestion that take place
without having to think about them are regulated by the
__________.
(A) somatic nervous system
(B) cerebrum
(C) neurons
(D) autonomic nervous system
18. Which factor is most important in determining how atoms of an
element will chemically react with other atoms?
(A) the number of electrons in the outer shell
(B) the number of neutrons in the nucleus
(C) the chemical symbol of the element
(D) the atomic mass
19. Our Sun is classified as what type of star?
(A) yellow dwarf
(B) white dwarf
(C) yellow giant
(D) white giant
20. Shale and sandstone are types of __________ rocks.
(A) igneous
(B) sedimentary
(C) metamorphic
(D) compound
21. A DNA (deoxyribonucleic acid) molecule is shaped like a
__________.
(A) sphere
(B) double helix
(C) oblate spheroid
(D) triple helix
22. A net force of 15 N is applied to an object that starts at rest and
accelerates to a velocity of 12 m/s in 4 seconds. What is the mass
of the object?
(A) 3 kg
(B) 5 kg
(C) 12 kg
(D) 15 kg
23. A lunar eclipse is caused by __________.
(A) an anomaly in the Moon's orbit
(B) solar flares
(C) the Moon passing between the Earth and the Sun
(D) the Earth passing between the Sun and the Moon
24. Earthquakes occur due to movement of plates in the Earth's
__________.
(A) asthenosphere
(B) lithosphere
(C) outer core
(D) lower mantle
25. Which of the following organisms has an exoskeleton?
(A) human being
(B) spider
(C) amoeba
(D) eagle
26. Our lungs convey __________ to blood cells and receive
__________ and __________ from blood cells.
(A) oxygen, carbon dioxide, water
(B) oxygen, carbon dioxide, nitrogen
(C) carbon dioxide, oxygen, water
(D) nitrogen, carbon dioxide, oxygen
27. A fireplace is sealed behind a clear glass screen to prevent sparks
and ashes from getting out. Nevertheless, a person sitting in front
of the fireplace will be warmed by the heat of the fire primarily
because some heat is still transferred by __________.
(A) convection
(B) radiation
(C) conduction
(D) osmosis
28. Sodium (Na), which is in Group 1 of the Periodic Table of the
Elements, and chlorine (Cl), which is in Group 17, will bond
together to form sodium chloride (NaCl). How will this compound
behave when dissolved in pure water?
(A) The molecules will group together to form large crystals.
(B) The molecules will separate into Na and Cl atoms.
(C) The molecules will separate into negatively charged sodium
ions and positively charged chlorine ions.
(D) The molecules will separate into positively charged sodium
ions and negatively charged chlorine ions.
29. Meteorology is the study of __________.
(A) meteors and meteorites
(B) weather
(C) the atmosphere and atmospheric phenomena
(D) the solar system
30. Human eggs are produced in the female's __________.
(A) uterus
(B) fallopian tubes
(C) cervix
(D) ovaries
Answers and Explanations
1. A
Prokaryotic cells, such as bacteria, do not have nuclei. Their genetic
material is contained within the main part of the cell body. Eukaryotic
cells do contain nuclei where all genetic material is contained.
Eukaryotic cells are plant, animal, fungi, and protist cells.
2. A
Terrestrial planets are those closest in composition to the Earth. Not
surprisingly, they are also the inner planets and those closest in
proximity to the Earth. Terrestrial planets have an inner core of metal
and rocky surfaces similar to the Earth's, though their atmospheric
characteristics can be vastly different from those of the Earth. Jupiter,
Saturn, and Neptune are outer planets.
3. C
The direction of velocity of the skydiver is negative for the entire time
period discussed in the question, but due to the release of the
parachute, the later velocity is smaller in magnitude. Since the
parachute acts against the direction of motion of the skydiver (as
established by the fact that the magnitude of the velocity is decreased
instead of increased), the acceleration must be positive, opposite in
sign to the negative velocity. Alternatively, this question can be
reasoned out as follows: the skydiver is falling and has a negative
velocity, therefore down is negative; parachutes slow down skydivers
by pulling them in an upwards direction, therefore the parachute
provides a positive acceleration.
4. A
The applied force of the elevator has to counteract the weight of the
load in order to ensure a safe, uniform velocity up. So the work done
can be calculated as W = (12,000 N) × (250 m) = 3,000,000 J. Power is
energy expended per unit time, so P = (3,000,000 J) ÷ (10 s) = 300,000
W.
5. D
The air in the troposphere is approximately 78% nitrogen and 21%
oxygen. This is the layer of air closest to the Earth's surface.
6. B
Animal cells have semi-permeable membranes which allow for
osmosis. Osmosis is essential for maintaining homeostasis within the
cell and preventing it from shrinking or bursting.
7. A
The troposphere is the lowest level of the atmosphere and where all
weather affecting Earth takes place. This is the level where clouds form
and from where precipitation falls.
8. C
The question asks for the statement about hydrogen which is not true.
Both answer choices (A) and (B) are true statements. (The atomic
number of 1 means there is one proton, and that one proton accounts
for the atomic mass, which is also 1). The question can now be
answered by identifying just one of the remaining statements as
definitely true or false. Since hydrogen is definitely not a noble gas
(helium is the lightest noble gas, with atomic number two), (C) is the
correct answer. Alternatively, (D) can be identified as the last true
statement (hydrogen has a single electron in its outer shell, like alkali
metals), which by process of elimination means that (C) is the correct
answer.
9. D
Mixing salt and sugar is a physical change. When mixed together, the
salt and sugar retain their molecular make up. Drying wet clothes is
also a physical change. When clothes are dried, water molecules
evaporate, becoming a gas. The clothes and water molecules remain
chemically unchanged. When boiling a pot of water, once again, liquid
water molecules move into the gas phase, but there is no change in the
chemical composition of the molecules. Finally, burning wood is a
chemical change, because the molecules in the wood are converted
into new molecules that are different than the original.
10. A
Air flow in the stratosphere is primarily horizontal, in contrast to air
flow in the troposphere, which has a strong vertical component.
11. A
Nuts and green leafy vegetables are a good source of magnesium.
Bananas, sweet potatoes, nuts, and seeds contain potassium. Milk,
yogurt, cheese, and spinach provide calcium. Meats, beans, and whole
grains are all sources of iron.
12. C
The speed of light is slower in water than in air causing light to bend at
the interface between air and water. While this may look like what
could be called an optical illusion, elusivity is not a phenomenon
related to light. Reflection would be due to light bouncing off a surface
such as a mirror. Rotation is irrelevant to this question.
13. C
Red blood cells are produced by the marrow inside human bones. The
liver has many functions, most of which are related to the digestive
system. Kidneys, in addition to their role in purifying blood, produce
the hormone that stimulates red blood cell production in the bone
marrow. The spleen stores and purifies blood.
14. A
Burning is a chemical change, not merely a change of a physical state.
Although most materials do not transition directly from a solid to a
gas, dry ice does, and the phase change is called sublimation. Sleet
melting is an example of a solid liquefying (melting). Morning dew is
the result of water vapor in the air condensing on the grass.
15. C
HIV can only be transmitted by an infected person's bodily fluids, such
as blood, saliva, or semen.
GENERAL SCIENCE PRACTICE SET 2
16. C
Because of the tilt of the Earth, during the summer months the Sun's
rays are more directly overhead and the days are longer; hence
summer is the warmest season. Because of the tilt, summer occurs at
“opposite” times of the year in the northern and southern
hemispheres. The distance between the Earth and Sun does vary, but
the effect on climate is much smaller than the tilt. The Earth is actually
farthest from the Sun during the months that those who live in the
northern hemisphere call summer. Solar winds are electrically charged
particles that, while they may be disruptive to electronic
communications, have little effect on climate. The Moon's position
affects tides, not climate.
17. D
The somatic nervous system controls voluntary actions and also sends
sensory information to the brain. The cerebrum is the portion of the
brain that is considered the center of intelligence. Neurons are
individual nerve cells.
18. A
Chemical reactions typically involve either the transfer or sharing of
electrons among atoms. Neutrons are in the nucleus, which usually
remains unchanged in chemical reaction (although the nucleus can be
changed in a nuclear reaction). The chemical symbol of an element
has absolutely no bearing on the element's properties. The atomic
mass is made up almost totally of protons and neutrons, so chemical
reactions have little to do with atomic mass.
19. A
Our Sun is technically classified as a G2V star, more commonly referred
to as a yellow dwarf because it is small relative to many other stars.
20. B
Sedimentary rocks are formed by the gradual deposit of sediments
over a very long period of time. The sediments could be sand, which
would form sandstone, or clay that could eventually become shale.
Igneous rocks originate as molten magma, and metamorphic rocks are
formed from other rocks altered by temperature, pressure, or chemical
processes. Compound is not a recognized type of rock.
21. B
The two biopolymer strands of DNA coil around each other to form a
double helix structure which, when the covalent bonds between the
strands are included, resembles a twisted ladder that bears no
resemblance to a sphere or oblate spheroid. Since there are only two
main strands, a triple helix configuration would not be possible.
22. B
Use Newton's second law of motion, F = ma, to solve this problem. The
object reached a velocity of 12 m/s in 4 seconds, so the acceleration
was = 3 m/sec2. 15 = m(3), so m =
= 5 kg.
23. D
When the Earth is exactly in line between the Sun and the Moon the
Earth's shadow is cast over the Moon, resulting in a lunar eclipse.
Eclipses have nothing to do with an anomaly of the Moon's orbit or
solar flares. When the Moon is between the Earth and the Sun, the
Moon's shadow falls on a portion of the Earth, resulting in a solar
eclipse.
24. B
The lithosphere refers to the Earth's crust and upper mantle, the two
layers closest to the surface. In order towards the center of the Earth
from the lithosphere are the lower mantle, asthenosphere, and outer
core.
25. B
The prefix exo– means outside, as in “external.” Human beings and
eagles have endoskeletons inside their bodies. An amoeba is a singlecelled organism that does not have a skeleton. A spider's outer shell
serves as its skeleton.
26. A
Blood carries the oxygen that cells need to function to the cells and
picks up the carbon dioxide and water that they generate, so the lungs
have to support that process by supplying oxygen to the blood and
carrying away carbon dioxide and water.
27. B
Heat is transferred by radiation when electromagnetic waves transfer
heat, just as we are warmed by the Sun. Convection transfers heat by
the actual movement of warmed matter, quite o en air. If the fireplace
were not sealed behind glass, heat would likely be transferred to a
room by convection. Conduction of heat occurs when two bodies of
different temperature directly touch. While the air touching the screen
will warm up and spread a very slight amount of heat into the space in
which the fireplace is located, that heat transfer would be very small
compared to the transfer by radiation. Osmosis, the passage of a fluid
through a membrane, is unrelated.
28. D
Elements on the le side of the Periodic Table, such as those in Group
1, have weak bonds with the electrons in their outer shells and will
give them up relatively easily. Elements in Group 17 are on the right
side of the table and have a strong attraction for electrons. Therefore,
compounds of atoms from these two groups will form ionic, rather
than covalent, bonds. When compounds with ionic bonds are
dissolved in water, they typically separate into charged ions. Since the
Na atoms have given up an electron, they will become positively
charged ions. The Cl atoms will retain an extra electron and become
negatively charged ions.
29. C
Watching meteorologists on TV presenting weather forecasts, one
could assume that meteorology deals exclusively with weather.
However, the science is much more broadly based, encompassing the
atmosphere as a whole. Although choice (A) might be tempting,
meteorology is unrelated to meteors.
30. D
The Latin word for eggs is “ova,” so it makes sense that eggs would be
produced in ovaries. From the ovaries, eggs travel through the
fallopian tubes where, if they are fertilized, they may implant in the
uterus. The cervix is located at the bottom of the uterus.
REVIEW AND REFLECT
As you look back over your work in this chapter, think about these
questions:
Which concepts are you more comfortable with, and which seem less
familiar?
As you worked practice questions in this chapter, were you careful to
make predictions whenever possible?
If you missed practice questions that called for calculations, was it
because you didn’t understand or remember the concept being tested
or because you made a misstep while doing the math?
Did you pay careful attention to the units required by a problem?
Which science topics should you review again before Test Day?
Want more practice with General Science? Log in at kaptest.com/login to
try more questions in the Qbank.
CHAPTER 10
ELECTRONICS INFORMATION
KNOW WHAT TO EXPECT
The discovery of electricity and its use in transferring energy has been the
foundation of modern technology. It’s hard to imagine a world without
automobiles, computers, or even flashlights. Though they have vastly
different functions, all electrical and electronic devices operate due to the
movement of subatomic particles called electrons (hence the word
electronics).
In this chapter, you will learn the basic principles of electricity and
electronic components. By the end of the chapter, you will be able to
identify some major circuit components and their functions, perform
calculations to determine circuit properties, and understand some of the
safety devices used in modern household wiring.
On the CAT-ASVAB, you will have 10 minutes to complete 15 Electronics
Information (EI) questions. If you take the paper-and-pencil ASVAB, you will
have 9 minutes to complete 20 EI questions.
Electron Flow Theory
Learning Objectives
In this section, you will learn to:
understand electricity as the flow of electrons through
conducting materials
understand the meaning of voltage, current, and resistance, and
how they relate to different aspects of electrical flow
A solid understanding of electricity begins at the atomic level. Matter is
composed of atoms, which are the smallest particles that elements can be
broken into and still retain the properties of that element. An atom is itself
broken into even smaller components, called subatomic particles.
Two subatomic particles are found within the nucleus: protons and
neutrons. Protons have a positive charge, and neutrons are neutrally
charged. The nucleus is the heaviest part of the atom and accounts for the
majority of the atom’s mass. Electrons, the third type of subatomic
particle, are in motion around the nucleus and have a negative charge. For
a neutral atom, there is one electron for each proton that resides in the
nucleus. From static shock to a lightning strike, all electricity is the
movement of electrons.
The electrons occupy various energy levels around the nucleus, known as
shells, and each time one becomes full, a new one is begun. The outer
shell of an atom is known as its valence shell, and the number of electrons
that reside in the valence shell are what determines whether an element is
a conductor, a semiconductor, or an insulator. In many elements, the
valence shell holds a maximum of eight electrons.
Boron, a Conductor; Silicon, a Semiconductor; and Phosphorus, an
Insulator
A conductor is an element that allows electrons to flow freely. What all
conductors have in common is one or more mobile valence electrons per
atom that are free to move from one atom to another, as each valence shell
has more empty spots than electrons. An insulator has a valence shell that
is more than half full or is completely full. It does not conduct electricity
much at all, because its electrons are all tightly bound and will not leave
their packed valence shells. A semiconductor, with a valence shell that is
exactly half full, is neither a good conductor nor a good insulator, but it has
some remarkable properties that make it very useful for making electronic
components.
A convenient way of visualizing how electricity works is to imagine the
electrons as drops of water flowing through a pipe. Such a flow is due to
applied pressure on one end, forcing the water the opposite way. Likewise,
when a conductor is connected across the terminals of the battery, the
negative terminal of the battery applies a repulsive pressure on the
electrons and pushes them toward the positive terminal. (A basic rule of
electricity is that like charges repel each other, while opposite charges
attract each other.) The resulting flow of electrons through a conductor is
an electric current.
CURRENT
The rate of flow of electrons through a conductor is known as current. Just
as the gush of water through a pipe has a current, so does the flow of
electricity. When you turn on a faucet, it’s easy to distinguish between a
trickle and a roaring flood by the very different amounts of water flowing
out each moment. Electrical current, similarly, is measured by the amount
of charge flowing past per unit of time. Current is measured in amperes, or
amps for short, and an ampere is defined as one coulomb (C), the basic
unit of electrical charge, flowing past a given point in one second. The
symbol used for amperes is A. If five coulombs of charge were to pass by a
point every second, this would be a current of five amps (5 A).
Try your hand at this EI question.
What would be the current if 18 coulombs passed by in
three seconds?
(A) 3 A
(B) 6 A
(C) 18 A
(D) 54 A
Explanation
The correct answer is (B). Since 18 C of charge pass by in 3 s (that is,
seconds), there must be 6 C passing by per 1 s. By definition, that’s a
current of 6 A.
One coulomb, incidentally, is the amount of negative charge in 6.25 × 1018
or 6,250,000,000,000,000,000 electrons. It takes this many electrons
flowing past a point in a conductor every second for a modest one ampere
of current to be flowing. Current can be measured using a device called an
ammeter.
VOLTAGE
In order to make electrons move through a conductor, there must be a
force that causes them to move. Water will move from a high-pressure area
in a pipe toward a lower-pressure area, but if the pressure is equal at both
ends, no movement takes place. Electricity is no different. There must be
electrical “pressure” applied to a conductor to cause electrons to move.
For an electron, the “pressure” is caused by electromagnetic repulsion
from a large negative charge, like that found at the negative terminal of a
battery. This negative terminal has a huge excess of electrons, all pushing
at each other. When a piece of conducting wire connects the positive and
negative terminals of a battery (known as “completing the circuit”),
electrons are pushed from the negative terminal into the wire, themselves
pushing along the conducting electrons already there, and so on down the
line, so that every electron will eventually reach the positive terminal,
where there is a shortage of electrons and an excess of attractive protons
pulling the electrons in. This will continue until the excess of electrons at
the negative terminal is exhausted, and the battery is dead.
Electrical pressure is known as voltage, and it is measured in volts
(symbolized by the letter V). The higher the voltage that is applied to a
conductor, the greater the electrical pressure the electrons will experience,
and the higher the current (rate of flow of electrons) will tend to be. Voltage
and current are therefore directly proportional.
To be more exact, voltage is really the difference in electric pressure
between two points, such that electrons will tend to be pushed from areas
of greater electric potential (the proper term for this pressure-like
quantity) to areas of lesser electric potential (lower pressure). For this
reason, voltage is also known as electrical potential difference. It’s also
referred to sometimes as electromotive force. A technician would
measure voltage using a voltmeter.
RESISTANCE
Opposition to the flow of current is known as resistance. Resistance is
measured in ohms, and one ohm is defined as the amount of resistance
that will allow one ampere of current to flow if one volt of electrical
pressure is placed on a conductor. The symbol for the ohm is Ω (the Greek
letter omega), and resistance can be measured using an ohmmeter.
As resistance in a conductor increases, current flow decreases. This means
that current and resistance are inversely proportional. The smaller the
resistance a material has, the better a conductor it is. But voltage and
current, remember, are directly proportional. Any time voltage increases,
current will also increase. So in materials with high resistance (that is, in
poorer conductors), a higher voltage must be used to get the same current.
All conductors have a certain amount of resistance, with some having more
than others. Three materials that are most o en used as conductors are
silver, copper, and aluminum. Of these three, silver is the best conductor,
as it exhibits the lowest resistance. Unfortunately, silver is relatively
expensive, so the next best choice is copper. Copper has only a slightly
higher resistance than silver, but is much less expensive. Most electrical
cable and wire is currently made from copper. Aluminum has a higher
resistance than copper, and exhibits some other characteristics that make
it even less than desirable for use in electrical applications. While
aluminum was used extensively in residential wiring at one time, it is now
used only in a few select applications.
EXCEPTIONS AND ADDITIONAL NOTES
The analogy of electron flow to the flow of water through a pipe is helpful,
but like all analogies, there are places where it breaks down. For example,
when a pipe is broken, water will spray out, but when a conducting wire in
an electronic device is broken, current flow simply stops along that path.
That’s because electricity travels through the conducting metal of a wire,
not inside a hollow pipe like water does. With no conducting material,
electrons cannot move forward, and air molecules are very poor
conductors. Except when the gap is very small (spark plugs are designed
this way) or the amount of voltage extremely large (as occurs with
lightning), an electric current will not flow through air.
Another interesting quirk in the study of electricity is what’s known as
conventional current, which is defined by the (imaginary) flow of positive
charge and is opposite in direction to actual electron flow. This strange
concept came about because of the difficulty in actually observing
electricity at a microscopic level.
Seeing and feeling the direction that water is moving in is easy enough, but
electricity is another story. When scientists first started studying electricity
seriously, not enough was known about atoms yet, and they realized that
either a flow of negative electrons in one direction or a flow of positive
protons in the opposite direction could explain the movement of charges
discovered to be at the heart of electricity.
Scientists took a guess that it was the protons that moved, and defined the
direction of current based on that. Later they discovered that protons stay
in the nucleus and don’t move, but current direction had already been
defined this way. As a result, if a circuit has a conventional current that is
moving in a clockwise direction, this means that, in reality, electrons are
moving around the circuit in a counter-clockwise direction. Nowadays, we
can refer to either conventional current or electron flow, but it’s necessary
to remember to switch the direction when going from one to the other.
It is straightforward to think of electrical current as a flow of electrons, but
an individual electron does not necessarily traverse an entire circuit. O en
this is more like a relay race as subsequent electrons carry the charge
onward. Some references may, therefore, refer to the flow of a charge.
This chapter hasn’t discussed circuits yet, but you still have enough
information to understand the worked example below. In the diagram, V
stands for a source of voltage, such as a battery cell, and L1 and L2 are
lamps connected to that voltage source. An unbroken line means an
unbroken connection, and a broken line means a broken connection.
Question
Analysis
In the wiring diagram pictured, which of the
Step 1: The question asks which lamp will
lamps will be lit up?
light up—that is, which will receive a flow of
current.
Step 2: The open switch (the break in the
middle line) prevents current from flowing
across the path containing lamp L1. That’s
because current cannot flow into a dead end.
However, the path from the battery cell,
through L2, and back to the opposite terminal
of the battery does make a complete circuit.
L1 should not have a current passing through
it, so will not be lit up. L2 should have a
current passing through it, so will be expected
to light up.
Question
Analysis
Step 3: Since there are no gaps in its path, L2
should be lit up, but L1 should not.
(A) L1 only will be lit.
Step 4: Choose option (B).
(B) L2 only will be lit.
(C) L1 and L2 will both be lit.
(D) Neither lamp will be lit.
Now try one on your own.
Certain conducting materials decrease in resistance as
the wires heat up. As resistance decreases, which of
the following would be expected to happen?
(A) The amount of current should increase.
(B) The amount of current should decrease.
(C) The direction of current should switch.
(D) The current should remain constant.
Explanation
The answer is (A). Resistance and current are inversely proportional, so
when resistance decreases, current increases. Remember that resistance is
so called because it resists current. If the resistance is less, it makes sense
that the amount of current is able to increase, similar to how the rate of
traffic flow is greater on the highway where there are fewer traffic lights.
Circuits
Learning Objectives
In this section, you will learn to:
effectively use Ohm’s law to perform circuit calculations
effectively use the power formula in an electrical context
recognize the features of a basic circuit and give definitions of each
simplify complex circuits
In order for electric current to flow, there must be a circuit for it to follow. A
circuit is a complete loop or path that electricity can follow. There are three
essential components of an electrical circuit: a voltage source, a load, and
conductors to connect the load to the voltage source. When these three
components are connected so that current can flow, we have a closed
(completed) circuit.
A load is basically a source of resistance that converts electrical energy into some
other energy form. For instance, a light bulb is a load. It has resistance and
converts electrical energy into light energy and heat. Other examples of loads are
electric motors, heating elements, and solenoids.
If a load’s resistance were to decrease, the current flowing in the circuit would
increase. However, if the circuit were broken, as in a wire (conductor) being
disconnected, no current would flow. This would be called an open circuit.
When current is flowing, each electron is carrying the voltage the length of the
conductor: pushing the electrons ahead of them to keep moving forward, while
being pushed themselves by those behind. When the line stops, it stops
everywhere, thus when there is no clear path to their destination, as in the gap
that occurs in an open circuit, electron flow stops entirely and the current is zero.
OHM’S LAW
The relationship between voltage, current, and resistance through a wire is
summed up in
Ohm’s law. Ohm’s law states that voltage (potential difference) in volts is equal to
the current in amperes multiplied by the resistance in ohms. This is represented
by the formula:
V = IR
V represents voltage, also known as potential difference, while I represents
current, and R represents resistance. If the I symbol seems odd, think of current
(defined as the amount of charge flowing past a point per unit time) as the
intensity of charge flow. The other two are easier to remember.
The voltage source is the beginning and end of the circuit. The negative side
repels electrons, forcing them to move through the circuit. The positive side helps
by attracting electrons, and an electron emitted from the negative side will
eventually traverse the complete circuit before arriving at the positive side.
Remember that voltage is essentially electric pressure on a charged object, so the
voltage source is ultimately responsible for electric flow in a circuit by pushing
the electrons forward.
To put it another way, a non-zero voltage will produce a certain amount of current
in a closed circuit for a given resistance, as shown by Ohm’s law above. Batteries,
which have positive and negative terminals, are voltage sources (for example, a
12 V battery). A household electrical socket also provides voltage, which
ultimately comes from the power plant. They are also referred to as power
sources, because the electric current they create carries energy.
The conductor is just the wire that connects the load(s) and voltage source. For
the sake of simplicity, the wire is o en considered to have zero resistance.
Although this is not true, the resistance in a conducting wire is o en small enough
compared to any given load that it can be ignored for most calculations. At zero
resistance, Ohm’s law requires the voltage across such a conducting wire to also
be zero, meaning the electrical pressure does not change from one side to
another.
Remember, a load is any component with resistance that converts electrical
energy into some other energy form. In accordance with Ohm’s law, were a load’s
resistance to decrease, the current flowing in the circuit would increase. However,
if the circuit were broken, as in a wire (conductor) being disconnected, no current
would flow. This would be called an open circuit. This, too, can be explained by
Ohm’s law, as the break or gap in the circuit is like a load with infinite resistance
(recall from the previous section that air is a terrible conductor).
SERIES CIRCUITS
An electrical circuit that has only one path for current to flow is known as a series
circuit. A break (opening) at any point in the circuit will cause current to stop
flowing in all parts of the circuit. The simplest possible circuit, one voltage source
connected to one load by conductors, is an example of a series circuit.
Series Circuit
Since there is only one path for current to follow in a series circuit, the current
flow will be the same in all parts of the circuit. It wouldn’t make sense, for
example, if one million electrons were leaving the negative terminal of a battery
each second, but two million were arriving at the positive terminal at the other
end. It would be like a plane taking off from New York and then landing in Miami
with twice as many passengers. Thus, the current passing through any single load
in a series circuit is the same.
I1 = I2 = I3 = . . .
On the other hand, what happens if multiple loads were found in a series circuit?
If two or more loads are added to a series circuit, their resistances add together,
creating what’s called the total or effective resistance across the circuit.
Rtot = R1 + R2 + R3 . . .
Voltage, which refers specifically to a difference in electric potential (“electric
pressure”) at two different points (like from the negative to the positive terminals
of a voltage source), can also be calculated across a single load. This is also
known as the voltage drop across a load, and the total of all voltage drops across
each load in a series circuit is equal to the total voltage of the complete circuit,
which is equal to the voltage of the voltage source itself.
Vtot = V1 + V2 + V3 . . .
Try applying these ideas to solve the following problem.
Three different loads with different rated resistances are
wired in series. Which of the following will be the same
through all of them?
(A) the voltage drop
(B) the resistance
(C) the current passing through
(D) the heat given off
Explanation
Choice (C) is correct. The current passing through one point in a series circuit has
to be the same in other parts of the circuit, as there is nowhere else for the
current to go.
PARALLEL CIRCUITS
It is much more common for loads to be wired in parallel. With this arrangement,
each load is wired in a separate path. If any one of these paths were to have a
break or gap, current flow would still continue through the other paths, so there
would still remain a closed circuit.
Parallel Circuit
Parallel circuits are the exact opposite of series circuits in that voltage is the
same throughout each parallel branch of the circuit, while current flow varies.
Since voltage is a measure of the difference in electric potential between two
points, the voltage across alternate paths connecting the same two points in a
circuit must also be equal.
V1 = V2 = V3 = . . .
On the other hand, current flow becomes divided when there are parallel paths.
It’s commonly misstated that electricity follows the path of least resistance. This
is not actually true. Electricity actually follows every possible path, though a
larger proportion of electrons will take a path of low resistance while a smaller
proportion will take a path with higher resistance. For a parallel circuit, therefore,
the total current through the circuit is equal to the sum of currents through each
closed path.
Itot = I1 + I2 + I3 . . .
What about the effective resistance of a circuit when multiple loads are wired in
parallel? It’s natural to instinctively think that adding more loads is bound to add
more resistance, but this is not the case. This is a little less intuitive at first glance,
so consider an analogy.
There’s a big sale on at a popular retail store. One of the aisles is choked with
customers trying to grab the best deal. The jostling customers, abandoned
shopping carts, and crates of items waiting to be shelved all create resistance,
making it difficult to move forward and slowing the rate at which people move
through the aisle. In this analogy, the people are electrons, and the rate at which
they move is the current value.
Suddenly, a store clerk clears away a pile of merchandise that was blocking an
adjacent aisle. This aisle, too, has a lot of junk in the way. It may even have higher
resistance than the original aisle, as it has more stuff. Even so, some shoppers opt
for that cramped but less crowded aisle. The total number of shoppers passing
through the store each moment is now greater, with the addition of that parallel
path.
Likewise, adding a load in parallel, even if that load’s resistance is high, decreases
the total or effective resistance of a circuit, because even though it has resistance,
it provides an additional path while doing nothing to constrain the existing one.
The formula for adding resistances in parallel is a slightly more complicated one,
but it’s very useful.
Study the example below.
Question
Analysis
What is the approximate amount of current
Step 1: The question asks for current through the
passing through switch S when it is closed?
whole circuit. Effective resistance of the circuit
and total voltage are needed to calculate this.
Step 2: There are two loads in parallel, so the
parallel resistances formula is needed.
Given the effective resistance (Reff), Ohm’s law can
be used to determine the current drawn.
The reciprocals of the resistance values are R1 =
and R2 =
. Find the least common
denominator and add:
Step 3: The predicted value is 6 A.
(A) 0 A
(B) 2 A
(C) 4 A
(D) 6 A
Now try one on your own.
Step 4: Select answer choice (D).
Which of the following would not increase the rate of direct
current flow, I, through a conductor?
(A) decreasing effective resistance via a variable resistor
(B) increasing voltage
(C) adding a resistor to the circuit in parallel
(D) adding a resistor to the circuit in series
Explanation
Answer choice (D) is correct. Using the process of elimination, (A) would decrease
the overall resistance of the circuit, which, according to Ohm’s law, would
increase current given a constant voltage source. Choice (B) would also increase
current flow if resistance remained constant. Choice (C) would also decrease the
overall resistance of the circuit and increase current. However, adding a resistor
in series would increase effective resistance, which means a decrease in current
drawn.
SERIES-PARALLEL CIRCUITS
The most popular arrangement is the series-parallel circuit. A series-parallel
circuit has some components, such as an on/off switch, wired in series with a
number of loads that are connected in parallel.
Series-Parallel Circuit
Most residential wiring circuits are series-parallel. Wall outlets are wired in
parallel, but are all fed from a circuit breaker (shown in the diagram as a fuse)
that is wired in series. Switching off the circuit breaker will turn off power to all of
the outlets. However, if the circuit breaker is on, voltage is provided to all of the
outlets whether there are loads plugged into them or not.
Determining the total effective resistance across a series-parallel circuit is a stepby-step process. Use the appropriate formula for each group of resistors, either in
series or parallel, to simplify the circuit to fewer and fewer calculated effective
resistances until a single value for resistance has been found.
To determine the voltage drop or amount of current flowing through any
particular load, combine Ohm’s law with the rules for current and voltage in
series and parallel wiring to solve for a given variable of any particular load.
Question
Analysis
In the diagram shown, all three resistors have a
Step 1: The question asks for the effective
resistance of 4 Ω. What is the effective resistance
resistance of a series-parallel circuit.
of the circuit?
Step 2: The two parallel loads can be combined
into a single effective resistance.
The effective resistance of the last two loads can
be added to the first load’s resistance since they’re
in series with the first load.
Step 3: The prediction is 6 Ω.
(A)
Ω
(B) 4 Ω
(C) 6 Ω
(D) 12 Ω
Step 4: Select choice (C).
Now try the question below on your own.
What is the amount of current passing through the 3 Ω
resistor in the circuit pictured?
(A) 3 A
(B) 4 A
(C) 6 A
(D) 12 A
Explanation
The answer is (B). Since a switch is open on the branch of one of the parallel 6 Ω
resistors, it can be ignored. That means this circuit will behave like a simple series
circuit. The two connected resistors sum to an equivalent resistance of 3 + 6 = 9 Ω.
Using Ohm’s law, the current flowing through the 3 Ω resistor (and one of the two
6 Ω resistors) can be calculated as I =
=
= 4 A.
ELECTRICAL POWER
Electrical power is a term that refers to the actual rate at which energy is provided
to and consumed by an electric circuit. Power is expressed in watts (joules per
second) and can be calculated by multiplying the voltage (in volts) applied to the
circuit by the current (in amperes) that flows in the circuit. This is represented by
the formula:
P = IV
Each electron flowing through a circuit or wire has energy. How much energy
depends on the voltage applied. Electrons moving through a large voltage have
more energy. On the other hand, a higher current means more electrons passing
by each moment. So an equivalent rate of energy delivery can be achieved by a
smaller number of electrons each moment (lower current) with a larger amount
of energy per electron (higher voltage), or a larger number of electrons each
moment (higher current) with a smaller amount of energy per electron (lower
voltage).
This formula applies not only to the rate of energy delivery (power found in longdistance power lines) but to the rate of energy production (power provided by a
generating plant) and to the rate of energy consumption (power usage of an
appliance or load). The word consumption is actually a little bit misleading, as
energy is never used up but just changes form. A forty-watt (40 W) light bulb
doesn’t really use up 40 joules every second. It transforms 40 joules of electrical
energy to 40 joules of light and heat energy each second.
Question
Analysis
Question
Analysis
An electric generator provides a power supply to a
Step 1: The question asks for the power of the
cabin at the North American household standard
generator.
of 120 V. If the effective resistance of the cabin’s
wiring is 30 Ω, what is the power usage of the
generator?
Step 2: Both current and voltage provided by the
generator are needed, but only voltage and
resistance are given. However, these can be used
to find current using Ohm’s law.
Now, power can be calculated.
Step 3: The predicted answer is 480 W.
(A) 4 W
Step 4: Select choice (C).
(B) 150 W
(C) 480 W
(D) 3,600 W
Now try a question on your own.
The power usage of a coffee pot is 1,200 W while running,
and is powered by a standard North American 120 V
electrical supply. What is the resistance of the coffee pot?
(A) 10 Ω
(B) 12 Ω
(C) 120 Ω
(D) 1,200 Ω
Explanation
Answer choice (B) is correct. Using the power law and solving for current, I =
= 10 A. Then using the current and voltage values in Ohm’s law and solving
for resistance, R =
= 12 Ω.
STANDARD ELECTRICAL UNITS AND THE METRIC SYSTEM
When using Ohm’s law and other electrical formulas, it is important to keep in
mind that the quantities used must be expressed in ohms, amperes, volts, and
watts. If any of these quantities are given in other units, these should be
converted before making calculations with them.
Any of these base units can be modified with metric prefixes. For example,
smaller generating plants typically measure their power output in megawatts
(MW), while cardiac doctors may measure tiny electrical signals in the human
heart on the scale of milliamps (mA).
For more detail on metric system prefix values, please refer to the measurement
information at the beginning of the Physical Science section of chapter 9: General
Science.
Structure of Electrical and Electronic
Systems
Learning Objectives
In this section, you will learn to:
explain the safety mechanisms that are used in modern
household electric systems
recognize the basic electrical components in a circuit via their
symbols
explain the basic functions of several electrical components and
their uses and benefits
Thus far, you’ve learned the basic operational and mathematical concepts
behind an electric circuit. In this next section, you will continue to build on
these skills. The section will include a discussion of different types of
current, some safety considerations, and components that give circuits
special qualities and enable them to perform specific tasks.
AC VS. DC
There are two types of current. They are direct current (DC) and
alternating current (AC). DC is current that flows in only one direction in a
conductor. This is the type of current that is delivered by a battery. Many
electronic devices, like cell phones and laptops, work on DC. AC is current
that changes direction (moves back and forth) many times in a second as it
moves in a conductor. Household electrical outlets deliver alternating
current. AC provides a more efficient way to transport electricity from the
power stations to your home or business.
Here in North America, AC is always delivered at 60 cycles per second
(hertz). One cycle would be voltage starting at zero, increasing to a
maximum level in one direction, then decreasing to zero, increasing to a
maximum level in the reverse direction, then returning to zero again. The
unit hertz (Hz) describes the frequency of the signal and is a measure of
how many complete cycles occur in 1 second. The figure below shows a 60
Hz AC signal.
60 Hz AC signal
This is the frequency equation:
f=
In the equation above, f = frequency in Hz and T = the amount of time for
one cycle in seconds. You can use that equation to solve for either
frequency or period when given one of them. Thus, with a frequency of 60
Hz, it can be determined that one complete cycle occurs in
of a second,
since:
T=
So, if power stations deliver AC and most electronic devices work on DC,
where and how does the conversion take place? Most electric devices come
with built-in AC to DC conversion systems. Later in this section, we will
introduce an electric component, the diode, that makes this conversion
possible.
GROUND
Grounding electrical devices and residential wiring is an important safety
factor. Ground represents a place of lowest potential in a circuit. Since the
potential difference (voltage) is largest between any point in the circuit and
the ground point, any “stray” electricity will follow this path since
resistance is low here. This is important to prevent shock due to external
influences such as lightning, or due to internal circuit failure where
conducting wires are compromised.
In residential wiring, ground is a common connection throughout the
wiring system that protects against electrical shock. All of the wiring
grounds are connected to an earth ground (such as a copper rod driven
into the ground or buried conduit) and this is used to guide electrical
current away from panels and equipment, should an internal short circuit
take place.
IMPORTANT ELECTRIC AND ELECTRONIC
COMPONENTS
The properties of a particular electrical circuit will change depending on
the types of components present. In this section, several of the major ones
are introduced and discussed.
Resistors
Not all components within an electrical circuit require the same voltage.
There are also times when it is useful to be able to raise or limit current in a
circuit in order to control certain functions (e.g., volume in a stereo). A
component that can be used to limit current and/or voltage is a resistor. A
resistor does what its name suggests: it creates a specific amount of
resistance that generates a voltage drop when current passes through it.
As you learned previously, resistance can influence current, via Ohm’s law.
An increase in R will therefore cause a decrease in the current.
Resistor Symbols
There are two major types of resistors used today: the fixed resistor and
the variable resistor. Fixed resistors, as their name implies, have a fixed
resistance. Variable resistors (rheostats or potentiometers), have
resistances that can be changed. Potentiometers are useful in changing the
voltage drop across a component in a circuit. In electronic applications,
they can be used to help adjust the volume on a TV, radio, or stereo.
Rheostats are useful in changing the current in a circuit and can be used as
light dimmers or to control the speed of small motorized devices.
Fixed resistors use a color band system to enable us to determine their
resistance in ohms. The first color gives the first number. The second color
gives the second number, and the third number gives the multiplier or the
number of 0s behind the numbers.
Fixed Resistor Color Bands
1st digit
2nd digit
Multiplier
1st stripe
2nd stripe
3rd stripe
Black
0
0
×1
Brown
1
1
×10
Color Name
1st digit
2nd digit
Multiplier
1st stripe
2nd stripe
3rd stripe
Red
2
2
×100
Orange
3
3
×1,000
Yellow
4
4
×10,000
Green
5
5
×100,000
Blue
6
6
×1,000,000
Violet
7
7
-
Grey
8
8
-
White
9
9
-
Color Name
So, given a resistor with a red, violet, and yellow band, what is the value of
the resistance? According to the chart, the red represents the number 2,
the violet represents the number 7, and the yellow represents 4 zeros.
Putting it all together, the indicated resistance is 270,000 ohms.
Given a simple series circuit with unknown resistance, how could you go
about determining the value of resistance in the circuit? This can be done
experimentally in one of two ways: first, by measuring resistance directly
using an ohmmeter. To use an ohmmeter correctly, remove the device with
unknown resistance from the circuit or disconnect the power source from
the circuit (an ohmmeter has its own power source). The resistance can
then be measured by attaching the ohmmeter leads across both ends of
the device.
Alternatively, if no ohmmeter is available, an ammeter connected in series
with the resistor and a voltmeter connected in parallel with the resistor as
shown below will give I and V. Via Ohm’s law, resistance is equal to V
divided by I.
Using an Ammeter and Voltmeter to Measure Resistance
Fuses and Circuit Breakers
An electric ground is one essential safety component in a circuit. It helps
prevent shock by providing an alternate path for electricity to flow, away
from the device. Fuses and circuit breakers are also important safety
components in a circuit. When current in a circuit increases too much,
wires can overheat, leading to fires.
A short circuit occurs when a load is bypassed with a conductor for some
reason. Since current and resistance are inversely proportional, the flow of
current will increase. This could be caused by something as simple as the
insulation on the wires leading to and from the load becoming frayed and
allowing the wires to come into direct contact with each other. If a short
circuit occurs in part of a series circuit, the net effect is merely to remove
the load that was bypassed as a result of the short circuit. If, however, the
short circuit occurs at any load in parallel circuits or bypasses all the loads
in series circuits, the resistance of the circuit as a whole is reduced to near
zero and a dangerous surge in current could occur. For this reason, it is a
good safety precaution to protect circuits with fuses or circuit breakers.
Fuses are thin wires that melt when current exceeds a prescribed amount,
thereby preventing any further electricity flow. This prevents any potential
damage to the electric device. One disadvantage of using a fuse is that
when it has melted, or “blown,” it has to be replaced before the circuit will
work again. Fuses with different current ratings can be used depending on
the device specifications.
Fuse Symbol
Circuit breakers serve the same function as fuses, but have the advantage
of being able to be reused multiple times. However, they respond more
slowly to increases in current than fuses do, and are more expensive to
install. There are several types of circuit breakers, but the underlying
principle behind their function remains the same. One class of circuit
breakers consists of a bimetallic strip that bends away from its contact in a
circuit when too much current is flowing. This makes a break in the circuit
and prevents further current flow. Another class of circuit breakers uses an
electromagnet to cause a breach in the circuit. When the current rises to a
certain value, the ferrous material is sufficiently magnetized to cause the
circuit to open, thereby inhibiting further current flow. Later in this chapter
we will explore the relationship between electricity and magnetism.
Circuit Breaker Symbol
Capacitors
Capacitors (also known as condensers) are electrical storage units. They
are constructed using two metal conducting plates with a very thin
insulator (known as a dielectric) between them. Air can also serve as a
dielectric.
Simple Condenser
A capacitor can store an electrical charge because the DC source creates an
excess of electrons on the negative plate and a shortage of electrons on the
positive plate. The electrostatic attraction between the positive and
negative charges keeps the charge intact in the capacitor, even when the
voltage source is removed. The capacitor will discharge itself if a conductor
is connected across it, as a path is then created for electrons to flow from
the negative plate to the positive plate. A capacitor will allow AC to flow
across it, but will block DC. This is why DC is most useful for “charging up”
a capacitor.
A capacitor’s opposition to the flow of current is known as capacitive
reactance, and this is measured in ohms. Capacitive reactance is inversely
proportional to the frequency of the AC signal. In other words, the higher
the frequency, the less opposition there is to the flow of AC across the
capacitor.
General Capacitor Symbol
Capacitance, or the ability of the capacitor to store charge, is represented
by the symbol C, and its unit of measurement is the farad. A farad is
sufficient capacitance to store one coulomb of electrons with an electrical
potential of one volt applied.
Question
Analysis
In the wiring diagram pictured, the fuse is
Step 1: The question asks what will happen to
rated for 0.1 A. When the switch is closed,
the lamp in the circuit when the switch is
what will happen to the lamp in the circuit?
closed; i.e., will it light or not?
Step 2: Normally, when the switch is closed,
current will flow and the lamp will come on.
However, this circuit has a fuse, so its impact
on the circuit needs to be considered. The
fuse is rated at 0.1 A. This means that it will
only allow currents to pass that are 0.1 A or
less. The current flowing in the current needs
to be determined.
Via Ohm’s law, I =
. Based on the circuit,
which is a simple series, V = 30V, and Rtot = 25
Ω + 35 Ω = 60 Ω . Thus, I =
= 0.5 A.
Question
Analysis
Step 3: Since the current in the circuit is
larger than the fuse’s 0.1 A rating, the light
may come on briefly, but the fuse will blow,
breaking the circuit and thus the light will go
off.
(A) The lamp will stay lit.
Step 4: Choose option (B).
(B) The fuse will blow, preventing the lamp
from staying lit.
(C) The fuse will stay intact, but the lamp will
go off.
(D) The lamp will blink continually.
Now try a question on your own.
A fuse rated at 0.5 A blows in a circuit when the switch
is closed. If the total resistance in the circuit is 100 Ω,
which of the following represents the smallest the
voltage could have been?
(A) 10 V
(B) 25 V
(C) 60 V
(D) 120 V
Explanation
Answer choice (C) is correct. If the fuse is rated at 0.5 A, it will blow when
current exceeds this amount. Via Ohm’s law, a 50 V power source in a
circuit with 100 Ω resistance would create a current of 0.5 A. Therefore, any
voltage above 50 V, such as 60 V, would blow the fuse. Choice (D) would
lead to a blown fuse as well, but the question asks for the smallest the
voltage could have been.
SEMICONDUCTORS
The term semiconductor refers to an element that has four electrons in its
valence shell. Since the bonds between these four electrons and the
nucleus are somewhat strong, these elements are neither good conductors
nor good insulators. Elements that are widely recognized as
semiconductors are silicon and germanium.
In their pure form, silicon and germanium are not particularly useful.
However, when impurities are added to their crystalline structure in a
process called doping, a whole new world of possibilities springs forth.
The crystalline structure of pure silicon is very stable. The four valence
electrons in each silicon atom bond with all the valence electrons in the
atoms around it, so no free electrons exist to allow current flow. This can
be changed by “doping” the silicon’s crystal structure with phosphorus,
arsenic, or antimony. Since these elements all have five electrons in their
valence shell, they will bond themselves to the other silicon atoms, but
leave one free electron that is able to migrate throughout the crystal. This
changes the silicon crystal into an N-type material. This new material is
still electrically neutral, but is able to conduct electricity due to the
presence of free electrons.
If silicon is doped with elements that have three electrons in their valence
shells (such as boron or indium), the result is a “hole” being le where an
electron would normally reside in the crystalline structure. This creates
repeating regions with an overall positive charge. As the free electrons
move into these spaces, they create “holes” in the spots they previously
occupied. With such doping, the silicon is now known as a P-type
material.
DIODES
P-type and N-type materials can do little by themselves; however, when
the two are joined, a diode is formed. A diode is an electrical one-way
valve that results from interactions at the junction of P-type and N-type
material. Current can pass easily in one direction, but is blocked in the
opposite direction.
Since current can only flow in one direction, the orientation of the battery
in a circuit is important. If current is able to flow, this is called forwardbiased. In order for the circuit to be forward-biased, the P-type material
(also known as the anode) should be connected to the battery’s positive
terminal and the N-type material (also known as the cathode) should be
connected to the battery’s negative terminal.
The excess of electrons at the battery’s negative terminal repels the free
electrons in the N-type material and sends them toward the junction. The
electrons in the N-type material then cross over the junction to fill the
“holes” in the P-type material, and current flows through the diode.
Reversing the diode’s connection to the battery creates a new set of
conditions. The N-type material’s free electrons move away from the
junction, since they are attracted to the opposite charge on the battery’s
positive terminal. Since the electrons have moved away from the junction,
no electron transfer takes place there and current flow stops. The diode is
now in a reverse-biased condition.
The most common application for diodes is rectification. Rectification is
the conversion of AC into DC. Since a diode only allows current to flow in
one direction, it will only pass either the upper or lower half of the AC
waves. This is known as half-wave rectification. Four diodes can be
connected in a diamond configuration to create a full-wave rectifier, which
is the foundation for most DC power supplies. Diodes are also used for
rectification in automotive alternators, where generated AC is converted
into DC to be used in the vehicle's electrical system.
Half Wave Rectification (Single Diode)
Full Wave Rectification (4 Diodes in Diamond Formation)
TRANSISTORS
The transistor is a component that has revolutionized the construction of
electronic devices such as computers, calculators and radios. A transistor is
versatile, as it can be used as an electrical switch, an amplifier, or a current
regulator. Since there are no moving parts in a transistor and it is made
from solid silicon, it is known as a solid-state device, which makes it very
reliable. It is also very compact in its design, as thousands of transistors
can fit into a single integrated circuit. An integrated circuit is one that
contains all necessary circuit components in one single silicon chip.
Transistors are the bedrock of logic operations that a computer uses to
process information.
There are two types of transistors: an NPN transistor and a PNP
transistor. An NPN transistor is made up of a thin piece of P-type material
sandwiched between two pieces of N-type material. A PNP transistor is the
opposite: two pieces of P-type material that have a piece of N-type material
between them.
Inside the transistor, wires connect to the three pieces of semi-conductor
material. Each piece is given a name. The middle piece is always called the
base; the two outside pieces are called the collector and the emitter. The
symbol for the transistor has an arrow that identifies the emitter. The
direction of the arrow tells us what type of transistor it is. The key to
remembering which symbol identifies which type of transistor is that the
arrow always points in the direction of the N-type material.
Symbols for NPN and PNP Transistors
The transistor works by using a small amount of current to control a large
amount of current. In the case of an NPN transistor, a positive voltage
applied to the base will “turn on” the transistor and allow a relatively large
current to flow from the collector to the emitter. The moment the positive
voltage is removed from the base, the transistor turns off and stops the
current flow.
Current Flow in an NPN Transistor
PNP transistors work opposite to NPN transistors. A PNP transistor requires
a negative voltage at the base to turn it on, and the current then flows from
the emitter to the collector.
Here are additional electronic component symbols that you may come
across when you take the ASVAB. Some of them, including transformers,
inductors, motors, and generators, will be discussed in the next section.
Wires and Connection Symbols
Power Supply Symbols
Switch Symbols
Output Device Symbols
Diode Symbol
Meters and Oscilloscope Symbols
Question
Analysis
Which of the following electrical components
Step 1: The question asks what circuit
can be used to convert the given input into
component is capable of receiving the input
the output shown?
signal and producing the output shown.
Step 2: The image shows AC as the input
being converted into DC as the output.
Step 3: A diode outputs only DC current. Any
AC current that is passed through a diode will
be converted to DC. Thus, only the positive or
negative values of the AC signal will be
output. None of the other electrical
components listed converts AC into DC.
(A) capacitor
Step 4: Choose option (D).
(B) fuse
(C) resistor
(D) diode
Now try a question on your own.
A capacitor is used to store charge. When a given
capacitor is “charged up” and then discharged, it will
output which of the following:
(A) direct current
(B) alternating current
(C) capacitance
(D) reactance
Explanation
Answer choice (A) is correct. A capacitor stores charge when a DC signal is
applied across it. When the capacitor is discharged, it can only output DC.
Electricity and Magnetism
Learning Objectives
In this section, you will learn to:
recognize the basic components in a circuit that function by
using the magnetic properties of electricity
explain the basic function of each of the electrical components
in this section and their use/benefit
Electricity and magnetism are closely linked. Moving charges produce
magnetic fields, and the moving electrons in a circuit are no exception.
From circuit breakers to transformers, from motors to generators, from
microphones to door bells, the interplay between electricity and
magnetism has proven useful in a range of applications.
A current-carrying wire generates its own magnetic field. The strength of
the field depends on the amount of current flowing in the wires. When the
wires are wrapped around a ferrous material and a current is passed
through the wires, the resulting magnetic field magnetizes the iron core,
producing an electromagnet. This induced magnetism is the basic
principle behind many of the aforementioned electrical devices.
INDUCTORS
The magnetic field formed by a current-carrying wire can be made stronger
by winding the wire into a coil. If the coil is wound onto a ferrous (iron)
core, the magnetic field around the coil becomes even stronger, since
magnetic lines of force travel more easily through iron than through air.
When current first flows through a coil, the magnetic field builds relatively
slowly. This is because the expanding magnetic field generates a voltage in
the coil that opposes the original current flow, known as counterelectromotive force, or counter-emf. When the current is cut off, the
magnetic field then collapses, and this collapsing magnetic field generates
a voltage in the coil that keeps the current flowing. This resistance to the
change in current flow in a circuit is known as self-induction and is a
property exhibited by electrical components known as inductors.
Inductors resist change in current flow. If current is increasing, the inductor
opposes the increase by generating a voltage that moves against the
applied current. If current decreases, the inductor uses the magnetic
energy in the coil to oppose the decrease and to keep the current flowing.
Inductor Symbol
Induction is measured in a unit known as henries, and the symbol used to
represent induction is L. Inductors work exactly opposite to capacitors, in
the sense that they allow DC to pass easily, but resist the flow of AC. This
resistance to current flow is known as inductive reactance and is measured
in ohms. It increases with increasing frequency of the AC signal.
TRANSFORMERS
A transformer is used to increase or decrease the voltage in a circuit. A
transformer uses the properties of an inductor to accomplish this.
Alternating current flowing in wires wrapped around an iron core
magnetizes the core, and in turn produces a changing magnetic field in the
core. This changing magnetic field generates a voltage in a neighboring coil
of wire. Depending on the number of turns of the wire in the primary
versus the secondary coil, and the proximity of the coils, a smaller or larger
voltage can be induced in the secondary coil. The primary coil is the one
that is connected to the source. The secondary coil is the one in which an
electric current is induced. A larger number of secondary coils means a
larger voltage. The closer the secondary coils are to the primary coils, the
more efficient the transformer is in producing a voltage in the secondary
coils.
Transformers are especially useful to transmit electricity from power plants
to residences and businesses. It is more energy efficient to transmit low
current, high voltage electricity. However, by the time it arrives at homes, it
must be reduced or “stepped down” to the standard 120–240 volts that
most appliances in our homes use.
BASIC ELECTRICAL MOTORS AND GENERATORS
A current-carrying wire positioned in a permanent magnetic field will
experience a force (push or pull). This force can be harnessed to produce
useful mechanical energy. This is the principle by which a simple motor
works. The mechanical energy can be used to move the tires on a car, spin
the blades of a fan, or li heavy objects, just to name a few examples. The
generated force on the current-carrying wire is directly proportional to the
amount of current flowing, the length of the wire, and the strength of the
magnetic field. Increasing any of these will increase the force on the wire
and thus the capacity to do work. Motors today are more complex than
this, and many use electromagnets in place of the current-carrying wire
alone, but the underlying principle remains the same. A generator, on the
other hand, is simply a motor in reverse. Moving a wire in a permanent
magnetic field induces a current in the wire if it is connected in a complete
circuit. Thus, a generator takes mechanical energy and converts it into
electrical energy.
Here’s how an expert test taker would approach a question about the
structure of electrical systems.
Question
Analysis
Given the following circuit, with a switch that
Step 1: The question asks what will happen to
has been closed for a long time, what will
the lamp in the circuit when the switch is
happen to the lamp immediately a er the
opened. Will it stay on or turn off? Burn less
switch is opened?
brightly or more brightly?
Question
Analysis
Step 2: Normally, in a simple series circuit,
when the switch is opened, the lamp will turn
off immediately. However, the presence of an
inductor in the circuit must be accounted for.
An inductor allows DC to pass easily with little
resistance, and so most of the current will
pass through the inductor and less through
the lamp. Thus initially, the lamp will not be
glowing very brightly. Once the switch is
opened, the current generated by the voltage
source will stop, but since the inductor resists
this change, it will briefly produce a voltage
that keeps current flowing in the circuit.
Step 3: Therefore, immediately a er the
switch is opened, the lamp will still stay lit
briefly and will burn more brightly, since all
the voltage generated by the inductor will be
dropped across it.
(A) The lamp will stay lit for a long time.
Step 4: Choose option (D).
(B) The lamp will burn more dimly.
(C) The lamp will immediately turn off.
(D) The lamp will briefly burn more brightly
and then turn off.
Now try a question on your own.
Which of the following circuit components, used when
electricity travels from power plants to residences, can
change the value of the input voltage, in a process
known as “stepping-up” or “stepping-down”?
(A) generator
(B) motor
(C) transformer
(D) inductor
Explanation
Answer choice (C) is correct. A transformer can take low current, high
voltage electricity from a power plant and reduce the voltage, or step it
down, before it enters a home. In general, a transformer can increase or
decrease the source voltage depending on the application.
Electronics Information Practice Set 1
Select the best answer for each question. This practice set contains
15 questions, which is the number of Electronics Information
questions you will see if you take the CAT-ASVAB.
1. How much current will flow in a circuit that has 60 mV applied to a
15 KΩ resistance?
(A)
(B)
(C)
(D)
0.004 mA
0.9 A
4.0 A
900 A
2. What voltage is required for 30 A to flow through a 60 kΩ
resistance?
(A)
(B)
(C)
(D)
1,800 V
1.8 kV
18 kV
1.8 MV
3. What is the current in the 20-ohm resistor?
(A)
amp
(B) 1 amp
(C) 30 amps
(D) 100 amps
4. Given the image below, which shell is the valence shell in a copper
atom?
(A) the first
(B) the second
(C) the third
(D) the fourth
5. Which is the collector in the transistor symbol below?
(A) 1
(B) 2
(C) 3
(D) 4
6. Current can be expressed in
(A) kilohms
(B) kilovolts
(C) milliamperes
(D) millivolts
7. A circuit with flowing current in it can be assumed to be
(A) open
(B) closed
(C) short
(D) dead
8. Which of the following symbols represents a polarized capacitor?
(A)
(B)
(C)
(D)
9. When a P-type material is joined with an N-type material, what is
created?
(A) a resistor
(B) a diode
(C) an inductor
(D) a capacitor
10. Which switch, if flipped, would not close the circuit in the diagram
shown?
(A) S1
(B) S2
(C) S3
(D) S4
11. Given a circuit with a single resistor, adding two more resistors to
the circuit, both with the same resistance value as the original
resistor, one in parallel with the original resistor, and one in series
with them both, will cause the overall resistance to
(A) definitely increase
(B) definitely decrease
(C) stay the same
(D) either increase or decrease depending on wiring order
12. Which of the following would not increase the rate of direct current
flow, I, through a conductor?
(A) decreasing effective resistance via a variable resistor
(B) increasing voltage
(C) adding an inductor to the circuit (in series)
(D) adding a resistor to the circuit (in parallel)
13. A circuit includes three 2 Ω resistors wired in parallel. What is their
effective resistance?
(A)
Ω
(B)
Ω
(C)
Ω
(D) 6 Ω
14. Why is copper favored over other conducting materials like
aluminum and silver?
(A) Copper has the lowest resistance.
(B) Copper has the highest resistance.
(C) Copper is inexpensive.
(D) Copper has low resistance relative to its cost.
15. A 6 V battery is used to provide power to a flashlight whose 10 W
light bulb is the only load in the circuit. What is the amount of
current flow through the flashlight?
(A) 0.6 A
(B) 1.67 A
(C) 6 A
(D) 60 A
ELECTRONICS INFORMATION
PRACTICE SET 2
Select the best answer for each question. This practice set contains
15 questions, which is the number of Electronics Information
questions you will see if you take the CAT-ASVAB.
16. A 2.5 V battery is used to power a cordless phone. An ammeter
shows the current flow is 30 A through the phone when it is on.
How much power does the phone use?
(A) 0.067 W
(B) 12 W
(C) 32.5 W
(D) 75 W
17. A shop vac is plugged into a 120 V generator. Given a total current
flow of 15 A, what must the total resistance of the vacuum cleaner
be?
(A) 8 Ω
(B) 15 Ω
(C) 120 Ω
(D) 1800 Ω
18. Two identical resistors are wired in parallel in a circuit. The voltage
drop across these resistors is 18 volts, and the total current in the
circuit is 6 amps. What is the resistance of either resistor?
(A) 1.5 Ω
(B) 3 Ω
(C) 6 Ω
(D) 9 Ω
19. Which of the following is one of the reasons neighborhoods are
connected to the power grid via electrical substations instead of
being wired into long-distance power lines directly?
(A) The substations use special components to connect aluminum
power lines to copper household wiring.
(B) The substation transforms direct current to alternating current
for household use.
(C) The substation transforms alternating current to direct current
for household use.
(D) The substation transforms the efficient high-voltage power
coming off the lines to a safer, lower value for household use.
20. A fixed resistor has a color band pattern of black, orange, orange.
What is its resistance?
(A) 33 ohms
(B) 3000 ohms
(C) 30,000 ohms
(D) 33,000 ohms
21. Given the following DC circuit, which has been open for some time,
what will happen a er the switch is closed?
(A) The total current flow will be smaller when the lamp first
lights, then increase dramatically.
(B) The lamp will light up brightly and then burn out.
(C) The countercurrent of the inductor will cause the closed
switch to spontaneously open again.
(D) The power draw on the battery will be higher at first, then
lower as the resistance decreases.
22. A European traveler brings his hair dryer to the United States. The
specifications on the small appliance say it draws 10 amps when on
a standard household circuit, which is 220 volts in Europe. What
will it draw if connected directly to a U.S. power source of 110 volts?
(A) 5 amps
(B) 10 amps
(C) 15 amps
(D) 20 amps
23. A portable air compressor converts electric energy to the potential
energy of pressurized air. A mechanics student calculates the total
energy of the pressurized air at about 800,000 J. If it took 400
seconds to fully pressurize the machine, what must be the electric
power rating of the compressor?
(A) 400 W
(B) 2000 W
(C) 800,000 W
(D) 320,000,000 W
24. Given a lamp wired in a simple AC household circuit, which of the
following will cause the light to dim the most?
(A) A capacitor wired in parallel with the lamp
(B) An inductor wired in parallel with the lamp
(C) A capacitor wired in series with the lamp
(D) An inductor wired in series with the lamp
25. In the circuit diagram pictured, where the two lamps have identical
loads, what will be the effect of closing the switch?
(A) L1 will light up and L2 will shut off; the power draw on the
battery will be the same.
(B) L1 will light up and L2 will dim; the power draw on the battery
will double.
(C) L1 will light up and L2 will remain at the same brightness; the
power draw on the battery will stay the same.
(D) L1 will light up and L2 will remain at the same brightness; the
power draw on the battery will double.
26. A simple parallel circuit with resistances of 2.5 Ω and and 5.0 Ω,
respectively, will have
(A) equal amounts of current through each resistor
(B) twice as much current in the 2.5 Ω resistor
(C) twice as much current in the 5.0 Ω resistor
(D) 100 percent of the current in the 2.5 Ω resistor
27. Plugs are o en differently shaped in different countries to prevent
foreign electronics from drawing on an electric grid they weren’t
designed for. What would happen if a device designed for a 150-volt
source were forced into a plug providing 240 volts?
(A) The device would function normally, as current and resistance
are constant within a device.
(B) The device might be weaker due to lower current.
(C) The device might burn out due to higher current.
(D) The device would function normally but waste more energy.
28. Which one of the following circuit components will least affect the
flow of an alternating current?
(A)
(B)
(C)
(D)
29. In the wiring diagram below, the fuse is rated for 0.4 A. The lamps
and resistor have the resistances given, and the fuse has no
resistance. What will happen when the switch is closed?
(A) Both lamps will stay lit.
(B) Both lamps will light briefly and go out.
(C) L1 only will stay lit.
(D) L2 only will stay lit.
30. A technician wants to measure the total current in the circuit
described in the wiring diagram shown. If she attaches ammeters
just a er the 10 Ω and 20 Ω resistors, the total current will be equal
to
(A) the sum of the values on each ammeter
(B) the value on either ammeter, since they’ll show the same value
(C) the difference in the values on the two ammeters
(D) the average of the values on the two ammeters
Answers and Explanations
ELECTRONICS INFORMATION PRACTICE SET 1
1. A
To solve this problem, the first step is to convert 60 mV to V. You can
quickly make this conversion by moving the decimal point three places
to the le , which yields 0.060 V. Next, convert 15 kΩ to Ω by moving the
decimal point three places to the right, which yields 15,000. Since
current is the unknown, the formula needed to finish the calculation is I
= E ÷ R. Dividing 0.060 by 15,000 gives 0.000004 amperes. This can be
converted to 0.004 mA.
2. D
Like the last problem, this one requires you to first convert the given
measurements. Take the resistance and move the decimal. 60 kΩ
becomes 60,000 Ω. Using our formula for calculating voltage, E = I × R,
we get 30 A × 60,000 = 1,800,000 V, or 1.8 MV.
3. B
The resistors in a series circuit add up, so one 40-ohm resistor in series
with a 20-ohm resistor is equal to a 60-ohm resistor. To find current flow
through a circuit, divide the total circuit resistance (60 ohms) by the
voltage across the circuit (60 volts) to get 1 amp.
4. D
The valence shell is the outer shell of an atom, which in a copper atom is
the fourth shell. A copper atom has 29 electrons, so it would fill the first
three shells completely and have one electron le to begin a fourth
shell.
5. B
In the symbol, the number 2 indicates the collector.
6. C
The ampere is the basic unit of current, so current can be expressed in
milliamperes.
7. B
A closed circuit has continuity and will allow current to flow in it.
8. C
The choices represent four different capacitor symbols: a fixed capacitor
(A), variable capacitor (B), polarized capacitor (C), and trimmer
capacitor (D).
9. B
When a P-type material is joined with an N-type material, a diode is
created.
10. D
Examine the diagram carefully. Notice that switches S1, S3, and S4 all
can direct current flow to either of two alternative paths. Switch S2 will
bridge the current from one of the top parallel paths to the other. The
circuit pictured is currently open. The S1 and S3 two-switches connect
to the same parallel paths, but presently, each is connected to a
different branch. If either of these switches were to flip, a complete
circuit would be made, passing through one or the other of these paths.
S2 is a simple on/off switch, and if closed, it too would close the circuit.
However, S4, a two-switch, cannot affect the current break in the circuit.
11. A
This question has no numbers, which can make it tougher to grasp. It
can be reasoned out if your understanding of parallel and series
resistors is very strong. Otherwise, your best bet in a situation like this
might be to just choose some simple numbers and do the math. The
question has three identical resistors in a series-parallel circuit. Choose
an easy number—three 1 Ω resistors would work just fine, and you can
determine the correct answer choice by seeing if the effective resistance
is greater than, less than, or equal to 1 Ω. The effective resistance of two
1 Ω resistors in parallel is
Ω. Add to this an additional 1 Ω resistor in
series, and the final effective resistance is
Ω, an increase. Time
permitting, the calculation can be repeated with a different resistance
value for the three resistors, just to ensure that the resistance still
increases.
12. C
Each answer choice would increase the rate of current flow, except one.
Answer choices (A) and (D) would both decrease the overall resistance of
the circuit, which, according to Ohm’s law, would increase current.
Answer choice (B) would also increase current flow if resistance was not
changed. However, for a direct current, an inductor in the circuit has
little effect. It will resist changes in current flow but not tend to either
decrease or increase it.
13. B
The effective resistance of several resistors wired in parallel can be
determined by taking the reciprocal of the sum of the reciprocals of
each individual resistance value. Since each resistor has a resistance of 2
Ω, you get
+
+
=
. Since the reciprocal of this sum is needed in
parallel resistor calculations, it’s best to stick with fractions at least until
the end. The reciprocal of
is simply the fraction created by switching
the numerator and denominator values, that is,
Ω.
14. D
Copper isn’t the best conductor. Silver has a lower resistance and is thus
better at conducting electricity than copper is. But though silver is a
somewhat better conductor, it is far, far more expensive. Copper is a
very good (but not the best) conductor, while also being very affordable.
Aluminum is inexpensive but is a worse conductor than copper. Copper
is also safer than aluminum, which, due to some of its heating and
expanding properties, is more likely to cause electrical fires in
household wiring setups.
15. B
Rearranging the power formula, I = P ÷ V = 10 ÷ 6 = 1.67 A (rounded to the
nearest hundredth).
ELECTRONICS INFORMATION PRACTICE SET 2
16. D
The relevant formula here is P = I × V, and both the current and voltage
are given, so P = 30 × 2.5 = 75 W.
17. A
The relevant formula here, V = I × R, needs to be rearranged in order to
calculate resistance. R = V ÷ I = 120 ÷ 15 = 8 Ω.
18. C
These two resistors are in parallel and can be treated as a unit. Since
we’re given the voltage drop across them both (the voltage drop either
in total or across either resistor is the same when they’re wired in
parallel), as well as the total current through them both, we can
calculate the total effective resistance of the two resistors. R = V ÷ I = 18 ÷
6 = 3 Ω. The question asks for the resistance of either resistor, though, so
there’s one more step. The formula for the total effective resistance of
these two resistors in parallel is
. However, since we
know both resistors are the same, and we know the total resistance, the
formula can be written as
. R is the resistance of a single
resistor and is exactly what we’re trying to figure out. Multiply both sides
of the equation by R to get
, or
. Then multiply both
sides by 3 to get R = 6 Ω.
Alternatively, you might recall that in the special case of multiple
identical resistors in parallel, you can use the shortcut of dividing the
individual resistance by the total number of resistors. In order to have a
total effective resistance of 3 Ω then, there must be two 6 Ω resistors (6 ÷
2 = 3).
19. D
Household wiring and long-distance high-voltage power lines are
connected via step-down transformers in the local substations. The
other statements are not true. The current is AC in both power lines and
household wiring, and power lines do not always use aluminum wiring.
20. B
The first and second color determine digits, and the last one determines
how many zeroes to add. Black is zero, then orange (in either of the first
two positions) is three, and then orange (in the final position) is three
zeroes. A zero at the beginning of the number has no effect, as 03000 is
just written as 3,000. Answer choice (C) would have been correct if the
pattern were orange, black, and then orange.
21. A
Inductors resist changes in current and for this reason act as resistors in
alternating current circuits. However, this property is also important in a
direct current circuit as seen here. An open circuit has no current, but
the moment the switch is closed, current will begin to flow. The
inductor, resisting the sudden change in voltage, will resist current flow
at first. The lamp, since it is parallel to the resisting inductor, will light up
immediately without difficulty. However, the inductor will soon “get
used” to the current flow, and the resistance of its path will drop
significantly. As more current flows through the easy inductor path, the
total current (and therefore energy use) of the circuit will increase
significantly as the overall resistance drops. (D) is exactly the opposite of
what will happen. Something similar to (B) could happen only if the
voltage source were limited in the amount of current it could provide
and the small fraction of current passing through the lamp were not
enough to light the lamp once the inductor dropped its resistance, or if
the total current draw caused a fuse or breaker to cut off the current.
However, in neither of these cases would the lamp itself “burn out.”
22. A
The hair dryer has the same resistance no matter what circuit it’s
attached to. You can calculate the resistance from the specifications
given and then use that same resistance to determine current under a
lower voltage. R = V ÷ I = 220 ÷ 10 = 22 ohms. Plugging this 22-ohm hair
dryer into an American socket gives you the current as I = V ÷ R = 110 ÷ 22
= 5 amps, which is answer choice (A).
Another way to answer this question is by reasoning it out from the
proportionality given by Ohm’s law: V = I × R. Given a constant
resistance, voltage and current are constant, so if the voltage is halved
from 220 to 110 volts, the current must also be halved from 10 to 5
amps.
23. B
This question about power takes you back to the more general
definition of power, as the rate of energy flow over time. You do not
need the electrical power formula, P = I × V. Instead, divide the total
energy, in joules, by the total time, in seconds, to determine the total
power, in watts. The information in the question is already given in the
correct units, so calculate 800,000 ÷ 400 = 2,000 W.
24. D
You can dismiss (A) and (B), since for loads in parallel, the voltage drop is
the same across all paths; the brightness of the light would not change if
the lamp were wired in parallel with either a capacitor or an inductor.
Loads in series, on the other hand, affect the overall resistance of the
circuit and therefore the total power draw on the battery. Recall that
capacitors and inductors can either let current flow freely or act as
resistors, depending on the type of current. In an AC circuit, a capacitor
lets current flow freely while an inductor resists current flow. An
inductor placed in series with the lamp will therefore act as a resistor
over which a voltage drop occurs, and the lamp will be correspondingly
dimmer than if the voltage drop of the circuit occurred entirely over the
lamp itself.
25. D
Before the switch is closed, there is only one path through the circuit,
through L2, so it is lit while the other lamp is dark. Closing the switch will
provide a second possible path, and as a result, both lamps will now be
lit. However, it’s also necessary to determine what will happen to the
brightness of L2 itself. The general rule is that lights in parallel will not
change their brightness as more paths are added, because the voltage
drop across each path remains the same and therefore the amount of
current passing through each lamp also stays the same. However, the
fact that there are now two lamps brightly lit instead of one does mean
that the battery will drain twice as fast because the total power draw of
the circuit will be doubled when the switch closes.
26. B
I = V ÷ R, and since the voltage across parallel loads is always equal, any
difference in current will be a result of the different resistances. You can
see that current and resistance are inversely proportional, meaning any
change to one will have the opposite effect on the other. But this
question may be a little easier to figure out by just making up a value for
voltage, say 5 V. Given this value, then, the currents through each load
will be I = 5 ÷ 5 = 1 A, and I = 5 ÷ 2.5 = 2 A. The 2.5 Ω resistor has twice as
much current as does the 5.0 Ω resistor.
27. C
Since the device’s resistance is constant, the formula V = I × R shows that
if voltage increases, current increases proportionally. To put it another
way, the greater the voltage, the greater the “pressure” pushing those
electrons forward. This has the effect of producing a higher current,
assuming the resistance is the same. Only answer choice (C) mentions
the higher current that must result from this situation. And yes, you
should definitely only plug your device into a socket that fits so you
don’t burn it out or start a fire.
28. B
This is the general symbol for a capacitor, which acts as a resistor to
direct current but does little to disrupt alternating current. It’s the
opposite of an inductor, pictured in answer choice (A), which acts as a
resistor to alternating current. Choice (C) is the diode symbol, which
allows current flow in only one direction. Since alternating current
constantly changes direction, half of the current flow would be
disrupted by the process known as rectification. Finally, choice (D)
displays an open switch, which will not allow either AC or DC power to
flow.
29. D
The total current in the circuit can be determined from the voltage
source and total resistance of the circuit. This is a tricky series-parallel
circuit that has to be taken in two steps. The total resistance of the
parallel loads L1 and L2 can be calculated without the full parallelresistors formula by using the rule that equal resistors in parallel have
an effective resistance equal to their individual resistance divided by the
number of parallel loads. The effective resistance of L12 then is 40 ÷ 2 =
20 Ω. This is in series with R, so the total resistance of the whole circuit is
20 + 10 = 30 Ω. Now, calculate the current draw of the circuit as I = V ÷ R =
30 ÷ 30 = 1 A. Once again, the fact that L1 and L2 have an equal amount
of resistance makes things easier. Since the two paths are equivalent,
each will take half the current, meaning 0.5 A passes through either one.
This is greater than the maximum current allowed by the fuse, so it will
burn out, cutting the current flow through L1 and leaving only L2 lit.
30. A
Current will separate when reaching parallel paths. Since the two
resistors are different, they’ll draw different amounts of current, so the
statement in (B) is false. However, regardless of whether they’re the
same or different, it’s the sum of the two currents that will give you the
total current. This technician would have been better off placing her
ammeter just a er the battery or perhaps near the switch, however, as
doing so would have allowed her to get the total current with a single
measurement.
REVIEW AND REFLECT
Look back over your work on these practice sets. If you struggled with
some of the questions, ask yourself why.
Did you misunderstand a formula or simply make errors in calculations? If
it’s the latter, be sure to slow down and double-check your math when you
do EIectronics Information questions. If you need to review the formulas
discussed in this chapter, consider making flashcards to help you
remember them.
Did you have trouble remembering some of the technical terms introduced
in this chapter? If so, consider making flashcards to help you memorize the
meaning of those terms.
Want more practice with Electronics Information? Log in at
kaptest.com/login to try more questions in the Qbank.
CHAPTER 11
AUTOMOTIVE INFORMATION
KNOW WHAT TO EXPECT
On the CAT-ASVAB, you are given 7 minutes to answer 10 Auto Information
(AI) questions. On the paper-and-pencil test, the Auto Information and
Shop Information subtests are combined into one, with 11 minutes to
answer 25 questions about both topics.
The required pace can be daunting. However, we’re confident that by the
time you finish this section, you will have a solid understanding of all of the
automotive systems and will be able to use Kaplan’s proven methods to
conquer AI questions. Take your time with this chapter, and remember that
you can’t possibly know everything a er one read-through. Review this
chapter multiple times if a high AI score is important to your career goals.
Also remember that there are many, many minute details involved in the
makeup of automotive systems. The test maker cannot possibly ask about
all of them. Your best approach to studying is to develop a thorough
understanding of automotive systems, their major parts, and how those
systems work together. This high-level understanding will likely equip you
to make solid inferences about details when you need to.
What’s in This Chapter
The modern automobile is a technological marvel. Thousands of parts are
assembled to form the means that many of us use for our daily
transportation. Space-age materials and advanced computer control
systems are used extensively in its construction, but in spite of all this, the
basic systems within the automobile still function the same as they always
have.
Despite its size, any automobile is still only made up of many smaller
parts. Parts are the smallest pieces that are used in the construction of the
automobile. Parts include such items as bolts, screws, spark plugs, and
belts. The parts of the vehicle cannot be disassembled any further, so they
form the foundation for the construction of the vehicle. Systems are
combinations of parts that work together to perform a particular function.
This chapter will be organized around four major types of systems:
Engine systems generate power to drive the vehicle’s wheels and
various accessories. The foundation of engine systems is engine theory,
which defines the mechanics and components involved in making the
engine run. Engine systems also include the cooling system, which acts
to remove excess heat from the engine. Finally, engine systems include
the lubrication system, which circulates motor oil through the engine to
reduce friction and make the engine run smoothly.
Combustion systems comprise the fuel system, which ensures that
correct amounts of air and fuel are available for efficient combustion in
the engine; the ignition system, which generates and times the spark
that initiates combustion; and the exhaust system, which forms a
“pipeline” for waste gases to be removed from the engine and then
dissipated to the open atmosphere.
Electrical and control systems are becoming more and more
significant in modern vehicles. These include the electrical system—
which includes starting, charging, lighting, and accessory systems—as
well as the computer system, which controls all aspects of vehicle
operation, including engine, drivetrain, brakes, and suspension.
Chassis systems are made up of the drivetrain system, which transmits
power from the engine to the vehicle’s drive wheels, the suspension and
steering systems, which control the vehicle’s ride quality and handling,
and the brake system, which stops the vehicle safely and predictably.
This chapter will conclude with a set of practice questions.
Engine Systems
Learning Objectives
In this section, you will learn to:
identify the basic function and the major components of the
internal combustion engine
differentiate between the different types and configurations of
internal combustion engines
identify the basic function and the major components of the
cooling system
identify the basic function and the major components of the
lubrication system
BASIC ENGINE THEORY
The type of engine used in automobiles is known as an internal
combusion engine. Combustion is the rapid burning of an air-fuel mixture.
Internal combustion means exactly that: fuel is burned internally and the
resulting heat is used directly to power an engine.
Typical fuels used with internal combustion engines are gasoline, diesel
fuel, propane, natural gas, and alcohol. Gasoline and diesel fuel are by far
the most common.
Three things must be present before combustion can take place: air, fuel,
and a heat source that can be used to ignite the air-fuel mixture. If any one
of those three elements is missing, combustion stops and the engine will
not run. Internal combustion engines convert the chemical energy in the
fuel and air into heat energy, and this heat energy is then converted into
mechanical energy. (See chapter 9: General Science and chapter 13:
Mechanical Comprehension for more information about types of energy.)
Components
There are common components in all internal combustion engines. These
components include:
Engine block: forms the framework for the engine cylinders and
reciprocating assembly.
Piston: a cylindrically shaped object with a solid crown (top) that moves
up and down in the engine’s cylinders. Hot gases produced from the
combustion of the air-fuel mixture push on the piston to do the actual
work.
Cylinder: forms a guide for the piston to move in; allows the piston to
move up and down as the engine completes its cycle.
Piston rings: seal the piston to the cylinder and prevent combustion
gases from leaking past. Oil rings prevent oil from the engine crankcase
from making its way into the combustion chamber.
Wrist pin: connects the piston to the connecting rod, and forms a pivot
point for the small end of the connecting rod to move on.
Connecting rod: connects the piston/wrist pin assembly to the engine’s
cranksha . The large end of the connecting rod attaches to the
cranksha on the connecting rod journal.
Cranksha : converts the linear (straight line) motion of the piston into
rotary motion, which can then be used to power a vehicle or drive an
accessory.
Cylinder head: located above the piston, it houses the combustion
chamber, the intake and exhaust valves, and the intake and exhaust
ports.
Combustion chamber: located in the cylinder head directly above the
piston, it is where the actual combustion of the air-fuel mixture takes
place.
Intake valve: allows the air-fuel mixture to be drawn into the
combustion chamber. When closed, it must seal the combustion
chamber from the intake port.
Exhaust valve: allows waste gases to be removed from the combustion
chamber. When closed, it must seal the combustion chamber from the
exhaust port.
Camsha : responsible for the opening and closing of the engine’s
intake and exhaust valves. The camsha turns at one-half the speed of
the engine’s cranksha .
Basic Engine Components
The conversion of linear (straight line) motion into rotary motion as
achieved by the piston-connecting rod-cranksha combination is very
similar to the leg of a bicycle rider. As the rider’s upper leg moves up and
down (piston), her lower leg (connecting rod), the bicycle pedals, and the
sprocket (cranksha ) convert that straight line motion into rotary motion
that then can be used to drive the wheels of the bicycle.
Most internal combustion engines are built to utilize a four-stroke
cycle. This means that it takes four strokes of the piston to complete one
cycle of events. A stroke of the piston is defined as the piston movement
from the top of its travel in the cylinder (top dead center or TDC) to the
bottom of its travel (bottom dead center or BDC) and back again to TDC.
The four-stroke cycle begins with the intake stroke. With the piston at
TDC, the intake valve begins to open. As the piston moves downward in the
cylinder, it forms a low-pressure area (or vacuum). Because the intake
valve is open to the atmosphere, air is sucked into the combustion
chamber due to the vacuum in the cylinder during the intake stroke. As the
air is traveling through the intake system, fuel is injected into the air stream
before it enters the combustion chamber. This allows the cylinder to fill
with a fresh mixture of air and fuel. Once the piston reaches BDC, the intake
valve is almost closed again and the engine is ready to begin the second
stroke of the cycle, the compression stroke.
During the compression stroke, the piston starts moving upward in the
cylinder while both of the engine’s valves are closed. With the combustion
chamber then sealed, the continued upward motion of the piston toward
TDC compresses the air-fuel mixture in the cylinder, as the air-fuel mixture
is forced into a progressively smaller and smaller space. The air-fuel
mixture in the combustion chamber becomes progressively hotter as the
particles of fuel get closer together due to the compression, making the airfuel mixture easier to ignite and ultimately increasing the power of the next
stroke, the power stroke.
Just before the piston reaches TDC of the compression stroke, the spark
plug fires and ignites the air-fuel mixture, starting a flame that then travels
across the combustion chamber. This flame further heats the gases in the
combustion chamber and the resulting rapid expansion of these gases
pushes on the piston as it passes TDC and then continues downward on
the third stroke of the cycle, the power stroke. During the power stroke,
both the intake and exhaust valves remain closed to ensure that the
pressure generated from the combustion of the air-fuel mixture is not
blown out past the valves but extracted by the motion of the piston toward
BDC.
Four-Stroke Cycle
Before the piston reaches BDC, combustion of the air-fuel mixture should
be completed. Just before the piston reaches BDC, the exhaust valve starts
to open and the engine begins its fourth and final stroke, the exhaust
stroke. The
gases in the combustion chamber are now spent and must be purged from
the engine before the next cycle can begin. As the piston begins its upward
movement, it pushes exhaust gases past the open exhaust valve and into
the engine’s exhaust system, where the exhaust gases are eventually sent
out to the open atmosphere. The piston continues its travel toward TDC,
and at that point will have completed one complete cycle of events. This
cycle then starts over as the intake stroke begins again.
Cylinder Arrangement
Automotive engines can be built in a number of different configurations,
and these can most easily be classified in terms of the engine’s cylinder
arrangement, which is the position of the various cylinders relative to
each other. The most common numbers of cylinders used in automobile
engines are four, six, and eight, but there are also designs that utilize three,
five, ten, twelve, and even sixteen cylinders.
The simplest cylinder arrangement is known as the inline design, in which
all of the engine’s cylinders are lined up in a row. This is a practical design
for four- and six-cylinder engines. Inline four-cylinder engines are very
popular in front-wheel drive cars with transverse (sideways) mounted
engines. Inline engines are most o en found in small- to medium-sized
vehicles. Another arrangement that has been utilized by engine designers
is the horizontally opposed or flat design. This arrangement has all of the
cylinders lying in a horizontal plane, with half of the cylinders facing away
from the other half and the cranksha located between them. Some refer
to this design as a “boxer” engine because the pistons move back and forth
like a boxer throwing punches. The one major advantage to this design is
that the engine’s center of gravity is much lower, so it is easier to build a
more stable, better-handling vehicle.
The last and most popular design for six- and eight-cylinder engines is the
V-type engine. These engines have one cranksha connected to pistons on
both sides of the V-shaped engine. The two rows of cylinders are located 60
to 90 degrees away from each other, and each row has one cylinder head,
for a total of two heads for the engine. A primary advantage of this
configuration is the inherent physical balance of the engine’s moving
components, resulting in a smooth-running engine. Another advantage is
the decrease in height and length relative to the in-line engine. The V-type
engine improves the aerodynamic flow outside the vehicle; because the
engine is smaller, the front of the vehicle can be lower. If an eight-cylinder
engine is needed, this configuration creates the power required while also
making the engine more compact.
Camsha Location
Another classification used to describe automotive engines is camsha
location. The camsha is responsible for the opening and closing of the
engine’s valves, and is driven by the cranksha through a timing chain or
timing belt. Some modern engines have the camsha located in the
engine block and the intake and exhaust valves located in the cylinder
head. Engines built in this manner would be known as overhead valve or
OHV engines because the valves are arranged above the piston and the
combustion chamber. In OHV engines, a lever called a rocker arm, which is
actuated by the camsha through a pushrod, operates each valve. The OHV
arrangement can be used with either V or flat configuration engines.
Engine designers o en locate the camsha above the valves and are then
able to eliminate the pushrods that are necessary for the OHV
configuration. The valve operating mechanism itself becomes simpler and
lighter. Less mass in the valve train means that higher engine speeds can
be attained. This design is known as the overhead cam or OHC. If only one
overhead camsha is used to operate the intake and exhaust valves of a
cylinder for an OHC engine, that arrangement is known as single overhead
cam or SOHC. In a V-type engine with two cylinder heads, there would be
two camsha s, with one installed above each cylinder head.
One final step to make even higher engine speeds possible is to go to a
double overhead cam or DOHC arrangement. This puts two camsha s
into each cylinder head, and makes it so one cam operates the exhaust
valves in that head, and the other operates all the intake valves. With this
arrangement, it is possible to eliminate the rocker arms that are o en used
in SOHC engines and have the camsha s operate the valves directly
through a follower.
Multiple-Valve Cylinder Heads
Engines may also be classified according to the number of valves used for
each cylinder. The least expensive and most common arrangement is to
use a two-valve cylinder head, with one intake valve and one exhaust
valve per cylinder. To improve airflow through the engine and, thus, engine
performance, it is possible to design a multiple (more than two) valve
cylinder head. Manufacturers have designed engines that use three valves
per cylinder, but now it is much more common to use a four-valve cylinder
head. This arrangement has two intake valves and two exhaust valves for
each cylinder. The four-valve cylinder head design has several advantages
over the two- or three-valve designs. The four-valve design allows higher
engine operating speeds and more complete combustion of the air-fuel
mixture, which helps improve engine power and efficiency.
Firing Order
The order that the cylinders fire in is known as the firing order. A common
firing order for four-cylinder engines is 1-3-4-2. This means that once the
first cylinder fires, the cranksha will make one half turn, and then the
third will fire and so on. Cylinders 1 and 3 will fire on the first turn of the
cranksha , and cylinders 4 and 2 will fire on the second turn of the
cranksha . In the case of a V-8 engine with a firing order of 1-8-4-3-6-5-7-2,
cylinders 1, 8, 4, and 3 will fire on the first turn of the cranksha , and 6, 5, 7,
and 2 will fire during the second turn.
Many engines have their firing order cast directly into the intake manifold
for easy reference. For those that don’t, it is necessary to refer to the
engine’s service information.
Diesel Engines
Another variation of the internal combustion engine is the diesel. Diesel
engines—also known as compression ignition engines—are much simpler
and more reliable than gasoline engines, mostly because they do not
incorporate a spark-ignition system. Instead of using a spark to initiate
combustion, diesel engines use a much higher compression ratio to
generate sufficient heat of compression to ignite the air-fuel mixture. The
compression ratio for a diesel engine can range anywhere from 16:1 to
22:1.
Another major difference between a diesel engine and most gasoline
engines is that all diesel engines must inject their fuel directly into the
combustion chamber or into a portion of the combustion chamber called
the pre-combustion chamber in order for combustion to take place. The
diesel engine must inject its fuel into the combustion chamber because it
needs the heat of the highly compressed air in the combustion chamber to
ignite the fuel, whereas all gasoline engines, including direct injected ones,
rely upon the spark-ignition system to initiate combustion.
Diesel Engine
Engine Operating Conditions
Air-fuel mixture
For an engine to run efficiently, it is necessary to mix air and fuel in the
correct amounts. Combustion suffers if there is too much fuel and not
enough air, or if there is too much air and not enough fuel. The ideal ratio
of air to fuel is known as the stoichiometric ratio, and it is the
responsibility of the engine’s fuel system to maintain that balance.
Air-fuel ratio is a comparison of the mass of the air relative to the mass of
the fuel that has been mixed with it. The stoichiometric air-fuel ratio for a
gasoline engine is 14.7:1. This means that 14.7 pounds of air is combined
with 1 pound of fuel to create an ideal air-fuel mix. When fuel is mixed with
air by the fuel system, particles of fuel are atomized and directed into the
air stream that is entering the engine.
Too much air and not enough fuel would be described as a lean mixture.
Lean mixtures burn relatively slowly because there is greater space
between the fuel molecules and it takes more time for a flame to jump
from particle to particle. Lean mixtures also burn much hotter, and thus
can cause serious engine damage. A typical lean air-fuel ratio might be
17:1.
In contrast, a rich air-fuel mixture has too much fuel and not enough air.
Rich mixtures burn quicker because of the small distances between fuel
particles, and they also burn much cooler. A rich air-fuel mixture can cause
spark plug fouling and black exhaust smoke, but is certainly less
threatening to an engine than lean mixtures. A typical rich air-fuel mixture
might be 10:1.
Ignition timing
Another major factor in making an engine run efficiently is ignition timing.
Ignition timing is the point in time during the combustion cycle that a
spark is generated at the spark plug. This is described relative to the
position of the engine’s cranksha . For instance, an ignition timing of five
degrees before top dead center (BTDC) would mean that the spark took
place when the cranksha was five degrees of rotation before top dead
center.
The spark is most o en timed so it will take place before the piston reaches
top dead center on the compression stroke, because it takes time for the
flame to move across the combustion chamber and burn the air-fuel
mixture contained within. By the time the air-fuel mixture is burnt, the
piston is on its way down again and is ready to make an effective power
stroke. Regardless of how fast the engine is turning, it will take
approximately the same amount of time for the flame to travel across the
combustion chamber. This means that for higher engine speeds, the flame
must be started earlier in order to generate the most effective downward
push on the piston. This is known as advancing the timing. An example of
an advanced timing would be 25 degrees BTDC. In this case, the spark
takes place when the cranksha is 25 degrees of rotation before top dead
center.
In contrast, retarding the timing means that the spark is adjusted to take
place later in the combustion cycle. Certain engine operating conditions
might call for a retarded timing as part of normal engine operation.
Ignition timing that is unnecessarily retarded, however, will have an
adverse effect on engine performance.
Combustion
Gasoline engine combustion is the rapid, thorough burning of a
compressed air-fuel mixture, initiated by a spark from the engine’s ignition
system. It is a flame that starts at the spark plug and then moves rapidly
across the combustion chamber, heating the gases and building pressure
in an even, controlled manner.
Normal combustion does not involve an explosion, and it is always
initiated by an electric arc at the spark plug. If combustion is started by
something other than an electric arc at the spark plug, this is an abnormal
condition known as pre-ignition. Pre-ignition takes place when the air-fuel
mixture is ignited prematurely (before the time the spark plug would
normally fire), typically by a hot spot in the combustion chamber, such as a
glowing spark plug electrode or a hot piece of carbon.
Detonation is when an air-fuel mixture explodes, rather than burns. It can
o en take place when an engine’s air-fuel mixture is lean. This is because
lean mixtures burn very slowly, and as the flame moves across the
combustion chamber, the unburned gases become heated due to the
advancing flame and the increasing compression in the cylinder. If the
temperature of these unburned gases rises sufficiently, they will “auto
ignite” and the flame front from this explosion will collide with the original
flame front. The pressure spike from this abnormal combustion results in a
brutal shock to the engine assembly, and can be heard as a “knock.” Severe
engine damage can result from unchecked detonation.
COOLING SYSTEM
There are two major types of cooling systems in modern automotive
engines. The first type is air-cooling, where air is circulated over cooling
fins on the outside of the engine to remove excess heat. The second type is
water-cooling. A water-cooled engine uses a liquid coolant to pick up
excess heat and then rejects that heat through a radiator. In order to ensure
optimized emissions and efficiency, cylinder temperatures need to quickly
reach operating temperature and remain consistent throughout a wide
range of ambient temperatures. Therefore, virtually all newly designed
automotive engines use liquid cooling, due to its greater flexibility in
coolant circuit design, its heat transfer ability, and its high heat capacity.
Coolant
The most critical component of the cooling system is the coolant itself.
Engine coolant is normally made up of a 50/50 mix of antifreeze and
water. Frozen coolant can lead to serious engine damage (even a possible
cracked block and/or cylinder head), so it is important that the coolant be
freeze-protected. The most common type of antifreeze is ethylene glycol. A
50/50 mix of ethylene glycol and water will not freeze until its temperature
reaches -34° Fahrenheit. This same 50/50 mix will also raise the boiling
point of the coolant, which is important in hot weather, because it makes
the coolant that much more efficient at transferring heat.
Components
The major components of a water-cooling system include:
Water pump: responsible for moving coolant through the cooling
system in order to transfer and control heat.
Water jacket: hollow sections in the engine block and cylinder head
that allow coolant to be transferred through them. These are the areas
that the coolant must absorb heat from.
Thermostat: controls engine temperature by allowing coolant to flow
into the radiator when the coolant temperature rises above a certain
level.
Bypass tube: allows coolant to flow back into the water pump from the
cylinder head when the thermostat is closed.
Radiator hoses: flexible hoses that allow hot coolant to flow between
the engine and the vehicle’s radiator.
Radiator: responsible for transferring heat from the coolant to the
outside air.
Radiator cap: responsible for maintaining pressure in the system, and
allowing coolant to transfer between the coolant reservoir and the
radiator.
Coolant recovery bottle: forms a reservoir for coolant to flow in and
out of the cooling system as the engine increases and decreases in
temperature.
Operation
Coolant is circulated through the engine by a belt- or timing-chain-driven
water pump. The engine cranksha drives the belt, so the water pump
actually uses engine power to operate it. The water pump takes coolant in
and pushes it into the engine block. The coolant then makes its way
upward into the cylinder head, and then returns to the inlet of the water
pump through the bypass tube. As long as the thermostat is closed (engine
is below operating temperature), the coolant will continue to circulate in
this manner.
When the thermostat opens, hot coolant moves past the thermostat into
the upper radiator hose, and then the coolant enters the radiator itself.
One of the methods used to raise the boiling point of the water has already
been mentioned: using coolants made up of a 50/50 mix of ethylene glycol
and water. The other method that can be utilized is raising the pressure in
the cooling system. The radiator cap is responsible for this, and most are
designed to maintain anywhere from 9 to 16 pounds per square inch (psi)
of pressure in the cooling system. For every 1 psi of pressure that is placed
on the cooling system, the boiling point of the coolant is raised
approximately 3°F. A 15-psi radiator cap would then raise the boiling point
of the coolant to between 212°F and 260°F.
Radiator caps incorporate two separate valves: a pressure valve and a
vacuum valve. As the engine warms up, the coolant in the cooling system
will tend to expand. This expansion will raise the pressure in the cooling
system, but when the pressure reaches the radiator cap’s rating, the
pressure valve in the radiator cap will li and allow some coolant to flow
from the radiator into the coolant recovery bottle. This flow will continue
as the cooling system pressure exceeds the rating of the radiator cap. The
coolant level in the recovery bottle will rise until the engine reaches
operating temperature.
When the engine is shut down and begins to cool, the coolant will contract
and create a low-pressure area inside the cooling system. If le unchecked,
this low-pressure area would cause the radiator hoses to collapse and have
an adverse effect on the cooling system at engine startup.
Maintenance
Cooling systems require maintenance in order to keep them operating at
peak efficiency. Again, the coolant itself is absolutely critical and making
sure to have it replaced every two to three years is a good maintenance
practice. The strength of the coolant should be kept at a 50/50 mix of
antifreeze and water. This will ensure that the coolant has sufficient freeze
protection and corrosion resistance.
It is also important to check that the belt driving the water pump is in good
condition, and that there are no leaks in the system. Hoses and the radiator
should also be inspected for visible signs of damage or wear. Most o en, a
leak will be external and can be observed as it drips from hose connections
or faulty cooling system components.
Comparison of Cold and Warm Engine Conditions on Automotive
Cooling Systems
LUBRICATION SYSTEM
Another system critical to engine operation is the lubrication system.
Without lubrication, the internal parts of the engine would very quickly
develop enough friction to stop (seize) the engine completely. The
lubrication system is responsible for the following functions:
Lubricates: It puts an oil film between moving parts to reduce friction
and smooth engine operation.
Cools: It puts motor oil in contact with hot engine parts (such as the
underside of the piston) and transfers heat to the oil pan, or the engine
oil cooler if applicable.
Seals: Motor oil acts as a sealer between the piston, the piston rings,
and the engine cylinder walls. This helps seal combustion gases in the
combustion chamber and makes the engine run more efficiently.
Cleans: Additives in the motor oil cause contaminants to be suspended
in the oil, so they can be filtered out by the engine’s oil filter.
Quiets: Motor oil damps engine noise and makes the engine run more
quietly.
Engine oil
Engine oil is a major component of the lubrication system. The engine oil
is the lubricant to the moving parts of the engine. The oil must be carefully
engineered to provide peak performance under the toughest engine
operating conditions, so choosing and using high quality engine oil is
extremely important for the life of an engine. Engine oil is made up of two
main components: base oil and an additive package.
One of the most important properties of engine oil is viscosity. Viscosity is
resistance to flow, and is expressed as a number that is directly
proportional to the thickness of the oil. The Society of Automotive
Engineers (or SAE) is responsible for developing the standards concerning
engine oil viscosity. Oil with a viscosity rating of SAE 5 would have a
relatively low viscosity (low resistance to flow), whereas SAE 50 oil would
have a high viscosity.
Another important engine oil rating system is the API quality rating. API is
the American Petroleum Institute, and it is responsible for setting
standards for engine oil quality. For a gasoline engine, this rating would
have a prefix of “S,” and then the next letter would identify the specific
quality standard that the engine oil meets. The first gasoline engine oils
produced had a quality rating of SA, but greater demands on engine oils
led to ratings that currently exist at the SN, SM, SL and SJ levels. Today’s
engines would not last very long if they were operated with an SA motor
oil.
Engine oil with a “C” prefix for its quality rating would be suited for diesel
engine use (e.g., a CJ-4, CI-4 plus, CI-4, and CH-4 rating). Engine oil that had
both an “S” and a “C” rating would be suited for either gasoline or diesel
engine use. An example of this would be engine oil with a rating of SJ/CD.
Components
The primary components of the lubrication system are as follows:
Oil pan: forms the reservoir for the engine oil at the bottom of the
engine.
Oil pickup tube and screen: immersed in engine oil, this filters out
large solids and directs oil into the oil pump.
Oil pump: responsible for pumping the oil through the engine oil
galleries. It is normally driven by the engine’s cranksha .
Pressure relief valve: prevents excessive pressure from building in the
lubrication system.
Oil filter: filters oil from the oil pump before it is sent to the various
parts of the engine.
Oil galleries: passages or “drillings” in the engine assembly that
transport oil to critical components.
Operation
There are two main designs for lubrication systems: dry sump and wet
sump lubrication. The dry sump system is very complex and typically only
used on racing vehicles and, therefore, is rarely encountered. Virtually all
mass-produced commercial and automotive engines use the wet sump
lubrication system design. In the wet sump system design, the engine’s oil
reservoir is located at the bottom of the engine in the oil pan. All oil used in
the engine drains to the oil pan due to gravity. There, it has an opportunity
to cool. The oil pump draws oil from the oil pan into its inlet through the
pickup tube and screen. The engine oil moves through the oil pump, and
then is transferred under pressure to the engine’s oil filter. The oil filter
removes particulates from the oil, and sends the clean oil on to the main
oil galleries.
When the engine is cold, the oil has a higher resistance to flow and thus
requires a good deal more energy to pump it through the system. This also
causes the engine’s oil pressure to rise. If the oil pressure rises above the
pressure relief valve’s setting, the relief valve will open and allow some of
the oil to drain back into the oil pan before it is pumped into the oil filter.
This prevents engine oil pressure from rising to the point where it can
damage components such as the oil filter, bearings, and engine seals.
The most critical area in the engine in terms of lubrication requirements is
the engine’s reciprocating assembly. The pistons, connecting rods, and
cranksha all require oil to lower friction and to remove heat. The largest
oil galleries in the engine are used to move oil to these areas, and galleries
are drilled directly through the cranksha to provide oil under pressure to
the connecting rod bearings. Oil that leaks off the connecting rod bearings
is thrown onto the cylinder walls, where it helps lubricate and cool the
pistons.
Other oil galleries take oil from the main oil gallery and direct it to the
engine’s valve train. This is where the camsha , li ers, push rods, rocker
arms, and valve stems get their lubrication. Other parts that may receive
lubrication from this oil would be the camsha drive, or timing chain, and
associated gear drives for the oil pump, ignition distributor, etc.
Oil that has circulated through the engine eventually drains back into the
oil pan. The oil pan is located at the bottom of the engine and thus sits low
in the engine compartment, where cooler air typically resides. This cool
outside air helps absorbs heat from the oil pan and helps cool the engine
oil. For heavy-duty or hot-weather operation, a liquid-to-air heat exchanger
(similar to the radiator in the cooling system) can be used to further cool
the engine oil. Once cooled, the oil is ready to be picked up by the oil pump
and circulated back into the lubrication system.
Maintenance
The key to lubrication system maintenance is to change the engine oil and
filter on a regular basis, and to use top-quality engine oil and filters. This is
the cheapest and most effective maintenance that can be performed to
minimize wear on the engine.
Questions on the ASVAB may ask you to recall or interpret how the various
systems of a vehicle operate. Let’s take a look at a sample question from
the area of engine systems, which encompasses engine theory, the cooling
system, and the lubrication system.
Question
Analysis
Question
Analysis
An internal combustion engine
Step 1: This question asks about
converts chemical energy of a
fuel into
energy to
power a vehicle.
the conversion of energy in an
internal combustion engine.
Step 2: The answer relates to
Engine Theory. Otherwise, there
isn’t much to simplify here.
Step 3: Recall that an internal
combustion engine converts
chemical energy of a fuel into
heat energy by burning the fuel
and then converts the heat
energy into mechanical energy
that is used to produce useful
work.
Question
Analysis
(A) electrical
(B) mechanical
(C) work
Step 4: The correct answer is (B).
Answer choice (A) is incorrect
because electrical energy is used
(D) sonic
to release the chemical energy
but is not the result of the release
of the energy. Choice (C) is
incorrect because work is the
result of the mechanical energy
produced by the engine. And (D)
is incorrect because even though
sonic energy (sound) is produced
in the energy conversion process,
sonic energy is not the source of
the engine’s power.
Now try a question on your own.
Engine coolant is normally made of a 50/50 mixture of
(A) water and soap solution
(B) salt and alcohol
(C) water and ethylene glycol
(D) antifreeze and saltwater
Explanation
Engine coolant is composed of 50% water and 50% ethylene glycol (also
known as antifreeze). The correct answer is (C). You would never want to
introduce a corrosive material like salt into an automotive engine coolant;
therefore, choices (B) and (D) are incorrect. Answer choice (A) is incorrect
because water with a small amount of soap solution added as a “wetting
agent” could function as an engine coolant, but not in a mixture of 50/50.
Soap does not increase the temperature performance of the coolant as
needed in automotive applications.
Combustion Systems
Learning Objectives
In this section, you will learn to:
understand the fundamentals of combustion within an internal
combustion engine
identify the basic function and the major components of the fuel
system
identify the basic function and the major components of the
ignition system
identify the basic function and the major components of the
exhaust system
FUEL SYSTEM
The fuel system is responsible for maintaining the correct air-fuel mixture
for efficient engine operation. If the air-fuel mixture is not adjusted
correctly, drivability, emission control, fuel economy, and engine service
life can suffer.
Up until about 35 years ago, it was most common for the air-fuel mixture to
be determined through mechanical means. This was accomplished
through the use of a carburetor, which was very reliable but incapable of
providing the precision required in modern fuel systems. Due mostly to the
demands of emission control regulations, the carburetor has been made
obsolete in favor of electronic fuel injection. This system is controlled by
an onboard computer and incorporates a feedback function that gives it
flexibility to adjust to changing engine conditions very quickly.
Components
The following are the major components of an electronic fuel-injection
system:
Electric fuel pump: located in the vehicle’s fuel tank; supplies fuel
under pressure to the fuel injectors.
Fuel filter: filters contaminants from the fuel before it reaches the fuel
rail.
Fuel rail: a manifold that supplies fuel under pressure to the inlets of all
the engine’s fuel injectors.
uel pressure regulator: regulates pressure in the fuel rail according to
intake manifold vacuum. Excess fuel is bled to the fuel return line, where
it is sent back to the fuel tank.
Fuel injector: sprays fuel into the intake air stream as it receives
electrical signals from the powertrain control module (PCM). The
location of the injector will determine the specific type of fuel injection
system being used on the engine.
Powertrain control module (PCM): another name for the vehicle’s
central computer. Responsible for control of all functions associated
with the engine and transmission.
Intake manifold: distributes air to the intake ports on the cylinder
heads.
Intake air filter: removes airborne contaminants that could damage
internal engine parts. All air entering the engine passes through the air
filter.
Throttle body/throttle plate: connected to the throttle pedal; controls
engine speed and output torque.
Fuel injection system designs
When fuel injection systems first came into common use, they were
designed to utilize either one or two injectors mounted in a throttle body
that took the place of the carburetor. This is known as a throttle body
injection system or TBI. While this system proved to be reliable, it was not
capable of providing a high enough level of fuel control to meet emission
control requirements. Most engines are now built with either multiport
fuel injection, which has an injector for each engine cylinder, or direct
injection, where the fuel is directly injected into the combustion chamber.
With multiport fuel injection, the injectors are located in the intake
manifold, with their spray directed toward the intake valves. As air enters
the intake manifold, it will flow all the way to the cylinder head before fuel
is injected into it. This allows for much better air-fuel mixing and prevents
fuel droplets from falling out on the intake manifold runners. With direct
injection, a high-pressure fuel injector is located to spray highly
pressurized fuel directly into the combustion chamber. Therefore, only air
flows over the intake valves and enters the combustion chamber. Fuel can
then be sprayed directly into the combustion chamber at an optimized
point in the compression stroke. Also, the fuel acts as a coolant to the hot
compressed air in the combustion chamber, which allows the engine to be
designed with even greater levels of compression, which further improves
power and efficiency.
Fuel Injection Types
Maintenance
The fuel-injection system requires very little maintenance. The filters (both
air and fuel filters) must be changed periodically, based on the
manufacturer’s recommendations. Manufacturers may also require
periodic cleaning of the injection system. Aside from that, fuel injection
systems are built to give reliable service with a minimum of maintenance.
IGNITION SYSTEM
One of the most critical vehicle systems is the ignition system. Without it,
combustion cannot take place, so the engine will not run. The ignition
system must generate high-voltage sparks at the correct time in order to
make the engine run smoothly and efficiently.
Components
The ignition system can be divided into two distinct subsystems: the
primary ignition system and the secondary ignition system. The primary is
the low-voltage part of the system, whereas the secondary is high voltage.
The following are the major components found in the primary ignition
system of a basic electronic ignition system:
Battery: supplies power to the ignition system for starting the engine.
Ignition switch: turns the engine on and off by switching power to the
ignition system.
Primary coil winding: the low-voltage winding in the ignition coil. This
is made up of several hundred turns of relatively heavy wire.
Ignition module: a transistorized switch that turns the primary current
on and off.
Reluctor and pickup coil: responsible for generating a signal that
operates the ignition module. The reluctor is mounted on the distributor
sha , and generates a signal in the stationary pickup coil as it rotates
with the distributor.
Distributor: driven by the engine’s camsha , the distributor is
responsible for timing the spark and distributing it to the correct
cylinder. Like the camsha , the distributor turns at one-half the speed of
the engine.
The following are the major components found in the secondary ignition
system of a basic electronic ignition system.
Secondary coil winding: the high-voltage winding in the ignition coil.
This is made up of several thousand turns of fine wire, wound around
the primary coil winding.
Coil wire: transmits high voltage from the secondary coil winding to the
distributor cap.
Distributor cap and rotor: directs high voltage from the coil wire to
each cylinder in the firing order. This is a switching mechanism that
allows one ignition coil to serve all the engine cylinders.
Spark plug wires: transmit high voltage from the distributor cap to each
spark plug.
Spark plugs: generate the spark to initiate combustion. They are
threaded into the cylinder head and protrude into the combustion
chamber.
Electronic Ignition Systems
Primary ignition operation
When the driver turns the ignition switch to the “run” position, current is
sent from the battery, through the ignition switch, and on to the primary
coil winding. From the coil winding, that same current flows through the
ignition module and back to the battery through the vehicle ground circuit.
Within the ignition system as a whole, the low-voltage (primary) system is
responsible for the control of the high-voltage (secondary) system.
Whatever happens in the secondary system is in response to the events in
the primary system.
The ignition system works because of a phenomenon known as
electromagnetic induction. If a magnetic field moves across a stationary
wire, voltage is induced in the wire. Another dimension of this principle is
that electric current passing through a wire will produce a magnetic field
around that wire. This means that electric current can be used to generate
a magnetic field, and a magnetic field can be used to generate electric
current.
Secondary ignition operation
The collapse of the magnetic field in the primary coil winding induces a
high voltage in the secondary winding. These secondary system voltages
typically range from 20,000 to 40,000 volts, and modern systems can go
even higher. This huge increase in voltage in the ignition coil is achieved
because of the large number of turns of wire in the secondary winding
relative to the primary. The magnetic field in the primary winding cuts
across a much larger number of turns of wire in the secondary, creating a
step-up effect in the coil.
The high-voltage current in the secondary winding must be directed to the
correct cylinder in the firing order. This current is directed through the coil
wire to the center tower of the distributor cap. From this point, it flows to
the rotor, which is mounted on top of the distributor sha and rotates with
the distributor. As the engine turns, the rotor will direct the current to the
appropriate cylinder and send it through the spark plug wire to the spark
plug. The electric arc at the spark plug is used to initiate combustion.
Current ignition system design
Since engine performance relies heavily on accurate ignition timing,
engineers look carefully at how to eliminate more moving parts from the
ignition system. This led to the elimination of the distributor in a design
named the distributorless ignition system or DIS. DIS systems use one
ignition coil to operate two spark plugs, so a V-8 engine would require four
separate coils instead of one. The increase in the number of coils allows
each coil more time to build up its electric charge and, therefore, deliver a
more powerful spark when the time comes to discharge. However, this
system still utilizes spark plug wires, which degrade over time and
eventually need replacement for the DIS system to function properly.
The most recent ignition system designs have eliminated the spark plug
wires altogether. These systems are known as coil-on-plug ignitions.
Individual ignition coils are mounted directly onto the spark plugs, and the
discharge of the coils is controlled by the vehicle computer system. While
the incorporation of computer control has increased ignition system
complexity, the elimination of moving and high-maintenance components
has led to very accurate control of spark timing, which is critical for
optimum engine efficiency and emissions, as well as increased reliability of
the ignition system.
EXHAUST SYSTEMS
The exhaust system is responsible for removing waste gases from the
engine. It must do this in a way that allows these gases to flow freely,
muffles the sound of the exhaust, and keeps the gases and heat away from
the vehicle cabin and its occupants.
Components
Typical components found in an exhaust system include the following:
Exhaust manifolds: attached directly to the exhaust ports on the
cylinder head. The majority of the exhaust heat and noise is focused on
the exhaust manifolds. These are o en made from cast iron for
durability under high heat conditions.
Catalytic converter: responsible for converting the toxic components of
engine exhaust into relatively harmless compounds such as carbon
dioxide and water.
Muffler: incorporates an expansion chamber and sound absorbing
material to diminish loud exhaust noises.
Tailpipe: the exit point for exhaust gases as they enter the open
atmosphere. The tailpipe normally exits at the rear of the vehicle.
Exhaust System Components
Operation
As gases flow from the exhaust ports of the engine, the exhaust manifold
collects them. On a V-type engine there would be two exhaust manifolds,
one for each cylinder head. These manifolds feed the gases into steel
exhaust pipes, which connect the major components of the exhaust
system.
The exhaust gases are then sent into the catalytic converter. High heat is
developed in the catalytic converter as it reduces the toxic components of
the exhaust to gases that are less toxic. Some vehicles use two, and even
three, catalytic converters in an effort to meet emission control
regulations.
A er leaving the catalytic converter, exhaust gases are directed into the
muffler. The muffler has expansion chambers built into it that absorb the
loud sounds generated by the engine’s combustion. The muffler is
normally located toward the rear of the car, somewhere a er the catalytic
converter and before the tailpipe.
Even a er passing through the catalytic converter, engine exhaust is highly
toxic. The most dangerous of the toxic gases emitted by the engine’s
exhaust is carbon monoxide, an odorless and colorless deadly gas. It is
extremely important that these gases be routed in such a way that they do
not come into contact with the driver or passengers in the vehicle. This
usually involves sending these gases to the rear of the vehicle where they
are dissipated to the open air by the tailpipe.
To increase engine efficiency and power, the exhaust system can be tuned
to match the design of the engine. “Tuned” exhaust manifolds are o en
known as header pipes. The idea is to allow exhaust gases to flow more
freely and allow the engine to breathe better. Increased performance is
usually gained at the expense of durability, as header pipes are much more
fragile than cast-iron exhaust manifolds.
Maintenance
The system should be inspected from time to time for physical damage;
there should be no restrictions and no leaks. The system should also be
tight in terms of its mounting brackets and clamps. Any damage should be
repaired immediately.
The catalytic converter will enjoy a long service life if the vehicle’s engine is
kept in good running order. An engine that burns oil or has ignition or fuel
system problems will damage the catalytic converter.
Questions on the ASVAB may ask you to recall the components or functions
of the various systems of a vehicle. Questions may be situational, asking
you to interpret the situation at hand and to make an assessment based on
your foundational knowledge of automotive systems. Let’s take a look at a
sample question from the area of combustion systems, which covers the
fuel system, the ignition system, and the exhaust system.
Question
Analysis
Question
Multiport fuel injection prevents
Analysis
Step 1: This question asks you to
recall one of the benefits of
multiport fuel injection.
Step 2: There is nothing to
simplify, but remember what you
know about multiport fuel
injection.
Step 3: One of the features of
multipoint fuel injection is the
ability to precisely atomize the
fuel into the intake air stream
within the intake manifold
runners. This fine atomization
enables the fuel to be suspended
in the intake air stream as fine
particles and prevents larger fuel
droplets from falling out onto the
walls of the intake manifold
runners.
Question
Analysis
(A) fuel droplets from falling out
on the exhaust valves
(B) fuel droplets from falling out
on the intake manifold runners
(C) the overheating of the engine
Step 4: The correct answer is (B).
Answer choice (A) is incorrect
because injected fuel does not
flow over the exhaust valve.
Choices (C) and (D) are incorrect
(D) engine fires
because, generally, multiport fuel
injection does not directly affect
engine overheating or engine
fires.
Now give this one a try on your own.
A major component of the primary ignition system is
the
(A)
(B)
(C)
(D)
reluctor and damper coil
inductor
primary resistor
reluctor and pickup coil
Explanation
The correct answer is (D). The reluctor and pickup coil are responsible for
generating a trigger signal that operates the ignition module. Answer
choices (A), (B), and (C) are not major components of the primary ignition
subsystem, and therefore are not correct.
Electrical and Control Systems
Learning Objectives
In this section, you will learn to:
identify the basic function and the major components of the
electrical system
understand the basic function and the major components of the
computer system
ELECTRICAL SYSTEM
The vehicle’s electrical system is growing in importance with each new
vehicle model year. Many systems that were once driven mechanically are
now being redesigned to operate electrically.
Subsystems
The major subsystems of the electrical system include the following:
Battery: stores electrical energy in chemical form. Provides direct
current (DC) for engine starting and accessory operation.
Starting system: responsible for cranking the engine to get it started.
The battery and starter motor are the major components of the starting
system.
Charging system: responsible for supplying electrical current to charge
the battery, as well as for vehicle operation. The major component of
the charging system is the alternator.
Lighting system: headlights, marker lights, brake lights, tail lights, etc.
Accessories: include the rear-window defogger, windshield wipers,
stereo, blower motors, and all other electrically powered accessories.
Battery
The battery is the foundation for the entire electrical system. It provides
electrical current for starting the engine, provides current to the electrical
system when the load exceeds the output of the alternator, and acts as an
electrical “shock absorber,” preventing voltage spikes when there is
excessive current in the electrical system.
An automobile battery is made up of lead plates immersed in an electrolyte
made up of sulfuric acid and water. This is why this type of battery is
known as a lead-acid battery. As the battery discharges, the sulfuric acid
in the electrolyte is reduced to water, and the lead plates become lead
sulfate. Charging the battery restores the chemical composition of the lead
plates and the electrolyte. Care must be taken when working with an
automotive battery because of the great amount of electrical energy and
the highly corrosive sulfuric acid stored in it.
Starting system
In order to start the engine, an electrically operated starter motor is
utilized. When the ignition switch is moved to the “start” position, an
electrical current is sent to the starter solenoid, which engages the starter
drive gear onto the engine’s ring gear (located on the flywheel). When the
drive is engaged, the solenoid connects the battery to the starter motor,
which then turns the engine at sufficient speed to start it.
Charging system
Once the engine is running, the charging system provides electrical current
to recharge the battery and power the vehicle’s electrical system. The main
component of the charging system is the alternator. The alternator is beltdriven by the engine’s cranksha , and converts mechanical energy into
electrical energy. The alternator produces alternating current (AC), which is
then rectified by an internal set of diodes known as the rectifier bridge.
The rectifier bridge converts AC to direct current (DC), which can be used to
power the vehicle’s electrical system.
A voltage regulator controls the output of the alternator. Normal system
voltage during engine operation is around 14.5 volts. Turning on the
headlights, heater motor, and other accessories on the vehicle increase the
load on the electrical system and system voltage drops. The voltage
regulator senses this decrease in system voltage and responds by
increasing the alternator’s output to compensate for it. As long as the
alternator’s output is able to match the load on the electrical system, the
system voltage will remain close to 14.5 volts.
Lighting system
There are many lights built into a vehicle’s lighting system. Headlights
illuminate the road ahead of the car, taillights mark the rear of the car for
other drivers, and interior lights help the driver see the instrument panel
and other areas inside the car when necessary. The various lights are
controlled by the driver through switches that turn the electrical current
to the lighting circuits on and off.
Fuses or circuit breakers protect the vehicle’s lighting circuits. If, for some
reason, the circuit should draw more current than it has been designed for,
the fuse will “blow” and cut off current flow. This protects the wires in the
circuits from overheating and may even prevent an electrical fire.
COMPUTER SYSTEM
Computer control systems work much like the human nervous system.
Sensors provide data to the computer, which processes this information
and sends signals to actuators to control vehicle functions. In the case of
the human body, the eyes and ears send signals to the brain, which
processes this information and sends signals to the various muscles to
control body movement.
Components
The major components of the automotive computer system include the
following:
Sensors: generate signals based on rotational speed, temperature,
pressure, and relative position. The sensors are the “eyes and ears” of
the computer system. An example of a sensor would be an oxygen
sensor, which is responsible for sending data to the computer
concerning the oxygen content of the exhaust gases. The computer uses
this information to determine whether the engine’s air-fuel mixture is
rich or lean.
Computer: processes data from the sensors based on a preprogrammed
strategy (so ware) and then generates outputs to control vehicle
functions. The computer is the “brain” of the computer system. In
today’s vehicles, the computer is o en referred to as the powertrain
control module (PCM) or the engine control unit (ECU).
Actuators: receive output signals from the computer and control vehicle
functions. An example of an actuator would be a fuel injector, because it
responds to signals from the computer to inject a specific amount of
fuel into the intake air stream.
Automotive technicians communicate with the ECU using a scan tool,
which allows them to get information from the computer concerning the
operation of the various vehicle systems. The scan tool is connected to the
vehicle’s computer system through a diagnostic data link that is typically
located near the driver’s seat.
Now, let’s look at how you will use your understanding of electrical and
control systems on Test Day.
Question
Analysis
Question
The alternator produces
current.
Analysis
Step 1: This question asks you to
recall the type of current
produced by the alternator.
Step 2: There is nothing to
simplify here.
Step 3: The rotating magnetic
field of the alternator rotor
produces an alternating current
(AC) in the alternator stator
windings. The AC produced by
the alternator must be rectified
into a direct current (DC) in order
to be compatible with the battery
and the rest of the vehicle’s
electrical system. The rectifier
bridge is the component that
performs the rectification of AC
into DC.
Question
Analysis
(A) fast
Step 4: Only answer choice (D)
(B) slow
(C) direct
addresses the nature of the
current produced by the
(D) alternating
alternator. So it is correct.
Now try another question on your own.
The PCM (or ECU) is the
system.
of the computer
(A) actuator
(B) sensor
(C) data link
(D) brain
Explanation
The correct answer is (D). The PCM (or ECU) is the processor that performs
the analysis of the sensor signals and sends control signals to the actuators
which makes the PCM (or ECU) the brains of the computer system. Answer
choices (A), (B), and (C) are supporting subcomponents of the computer
system that do not perform any analysis. Therefore, they do not answer the
question.
Chassis Systems
Learning Objectives
In this section, you will learn to:
identify the basic function and the major components of the
drivetrain system
recognize the basic function and the major components of the
suspension and steering systems
understand the basic function and the major components of the
brake system
DRIVETRAIN SYSTEM
The engine can produce power to move the vehicle, but this energy must
be processed and transmitted effectively in order to accelerate the vehicle
smoothly and quickly. Transmitting power from the engine to the wheels is
the responsibility of the vehicle’s drivetrain.
An important part of any drivetrain is the transmission. The transmission
is the device that matches engine speed to a desired speed of the vehicle.
The two main types of transmissions are the automatic and the manual.
Drivers who like to have more control over the operation of the vehicle will
o en choose a manual transmission, because the driver is responsible for
shi ing the gears up and down. A car with an automatic transmission is
much easier to operate because it does not use a driver-operated clutch
and does all of the gear shi ing automatically.
While rear-wheel drive was the most common design in years past, frontwheel drive has become very popular, especially in small- to medium-sized
cars.
Components
The typical components found in a front-wheel drive vehicle with a manual
transmission include the following:
Clutch: transmits torque from the engine to the transmission. The
clutch can be released and engaged to allow smooth starts and
transmission shi ing.
Transaxle: has several “gears” that are selected according to the speed
of the vehicle and how fast the driver would like to accelerate. The
transaxle is a combination of the transmission and the drive axle,
which are normally two separate components in a rear-wheel drive
vehicle.
Half sha : a short drive sha that transmits power from the transaxle to
the drive wheels. Used mostly in front-wheel drive vehicles, the half
sha s must be able to apply power to the drive wheels while allowing
them to move up and down and turn the vehicle. There are two half
sha s, one for each drive wheel.
Constant-velocity (CV) joints: can transmit power through very steep
angles, and are located at each end of a half sha . The inboard CV joint
is located at the transaxle, while the outboard CV joint is located behind
the vehicle wheel.
Rear- and Front-Wheel Drive
Other drivetrain components that may be found in other vehicle designs
include the following:
Transmission: used in rear- and four-wheel drive vehicles, the
transmission is responsible for matching engine speed to the desired
speed of the vehicle.
Drive sha : a longer version of the half sha , the drive sha transmits
torque from the transmission to the drive axle. The drive sha is also
required to allow up and down movement of the vehicle’s wheels, but
not to the same extent as the half sha in a front-wheel drive.
Universal joints: located at each end of the drive sha , the universal
joint allows the sha to operate at an angle with the component that it
is driving. Also known as U-joints.
Drive axle: transmits engine power through a 90-degree angle, and
splits that power between the two drive wheels. The wheels are
attached to the ends of the drive axle. The drive axle incorporates a
differential, which allows the le and right wheels to turn at different
speeds as the vehicle goes around a corner.
Transfer case: located between the transmission and the drive axles on
a four-wheel drive vehicle. The transfer case splits the engine’s power
between the front and rear drive axle.
Gear selection
Transmissions are built with several forward ratios that are based on the
specific gears that are used. Typical transmissions are therefore said to
have “speeds” or “gears.” For instance, a four-speed transmission would
have four forward gear ratios and one reverse ratio. A driver would typically
start from a stop using low (first) gear. In this gear, the transmission would
increase the torque from the engine sufficiently to be able to start the
vehicle from a standstill. However, this would limit the vehicle’s speed once
it did start rolling, so the driver would then select second gear and so on
as the vehicle continued to accelerate.
High (fourth) gear would be used to allow the vehicle to cruise on the
highway. Engine speed would be moderate to low in this gear, allowing for
maximum fuel economy and quiet running. To accelerate quickly, however,
the driver would downshi to a lower gear in order to increase engine
speed and power. Proper gear selection is important when operating a
vehicle with a manual transmission. Modern transmissions now have as
many as eight forward speeds.
Automatic transmissions
Automatic transmissions are much more complex than their manual
counterparts, yet are much easier to operate. The reason that many drivers
prefer them is that automatic transmissions do not use a driver-operated
clutch.
Instead of using a clutch, automatics transmit engine torque from the
engine to the transmission through a torque converter. The torque
converter uses fluid to transmit power, and allows for a certain amount of
slippage when the vehicle is stopped.
Automatic transmissions do all of the gear selection for the driver. This is
done in the transmission using hydraulic pressure to select the proper
planetary gear sets. Virtually all modern automatic transmissions are
controlled electronically by the vehicle’s powertrain control module.
Another modern automatic transmission is the continuously variable
transmission or CVT. A CVT transmission does not utilize specific gear sets
to determine the transmission ratio (or gears). Instead, it relies on two
opposing sets of cones, one for input and one for output, with a chain or
belt running between the two cones. The effective ratio of the transmission
depends on where the chain (or belt) is riding on the two cones. Because
the transmission’s effective ratio is not limited to specific gears as in a
typical transmission, the ratio can be varied continuously between the
limits of the diameters of the two cones.
Torque Converter
SUSPENSION AND STEERING SYSTEM
The newest suspension and steering systems have incorporated computer
control in an effort to improve vehicle performance. While the
sophistication of computer control has increased the overall complexity of
these systems, the basic principles remain the same.
Components
The major components of the long-short arm suspension system include
the following:
Springs: hold the vehicle’s chassis up and allow the wheels to move up
and down in relation to it.
Shock absorbers: absorb the energy released by the up-and-down
movement of the vehicle wheels.
Control arms (A-arms): the long-short arm suspension system uses an
upper and lower control arm to maintain the vertical orientation of the
steering knuckle as the wheel moves up and down.
Steering knuckle: connects to the upper and lower control arms
through the use of ball-joints. The wheel hub mounts on the spindle,
which is part of the steering knuckle.
Ball joints: ball-and-socket assemblies that allow the steering knuckle
to turn and move up and down simultaneously.
Steering linkage: connects the steering wheel to the steering knuckle.
Wheel hub: forms the mounting point for the vehicle’s tire assembly.
Tire: makes contact with the road and provides a “footprint” to aid in
vehicle stability and handling.
Long-Short Arm Suspension
Construction and operation
In order to make a vehicle ride smoothly, the wheels must be able to move
up and down while the vehicle chassis stays steady. This is the job of the
vehicle springs; they must be able to allow this movement of the wheels
without transmitting road shock. However, the springs absorb energy as
this happens and must release this energy without bouncing the vehicle
a er encountering a bump.
The shock absorber is installed between the chassis and a control arm to
help dissipate or absorb the energy stored in the spring as it is either
compressed (or jounced) or extended (or rebounded). Without properly
functioning shock absorbers, the vehicle will continue to bounce up and
down a er the vehicle has hit a bump in the road. The shock absorber uses
a piston and hydraulic oil to absorb the excess mechanical energy from the
suspension system and then releases that same energy in the form of heat.
The upper and lower control arms form the supports for the steering
knuckle. The control arms are attached to the chassis through the use of
control arm bushings. The spring is placed between the chassis and one
of the control arms. The spring can be installed on either the upper or
lower control arm in a long-short arm suspension. The control arm with
the spring on it becomes the load-bearing arm as the vehicle weight is
supported through it on the way to the steering knuckle and tire assembly.
An upper ball joint and a lower ball joint are used to attach the steering
knuckle to the control arms. Ball joints are built similar to a human hip
joint, with a ball and stud rotating in a socket to allow a wide arc of
movement. As the control arms move up and down, the ball joints allow
the steering knuckle to move freely with them. They also allow the steering
knuckle to turn le and right as it is moved by the steering linkage.
The steering linkage forms the connection between the steering wheel
and the steering knuckle. There are two main designs in common use, the
linkage steering and the rack and pinion. Long-short arm suspensions
most commonly use linkage steering to connect the steering column to the
pitman arm, center link, and idler arm. Tie rods are then used to make
the final connection to the steering knuckles. Smaller vehicles most
commonly use the rack-and-pinion steering system because it is the most
compact of the two major steering systems.
Linkage Steering
Rack and Pinion Steering
Tires
Tires are one of the most critical components of the suspension and
steering system. They support the weight of the vehicle and make final
contact with the road surface. The most common tire design is the radial
tire, which is known for its stable footprint and low rolling resistance.
Tire construction begins with the beads. The bead is a circular piece of
high strength material like steel wire that is encased in rubber. The bead
forms the mounting point for the tire on the rim. Body plies form the main
body of the tire and run from bead to bead. All other parts of the tire attach
to the body plies, including the liner (sealed surface inside the tire), the
sidewalls, and the tread.
Belts are used between the plies and the tread to help stabilize the tire’s
footprint (where the tire makes contact with the road). A stable footprint
means better traction under all road conditions, and makes the vehicle
handle and brake better.
Maintenance
The primary maintenance that should be performed on suspension and
steering systems is lubrication of the ball joints, tie rod ends, and other
components. This should be done with a hand-powered grease gun, and
the amount of grease should be metered carefully.
The most important part of tire maintenance is proper inflation. Low
inflation pressures can be very dangerous as well as increase the rolling
resistance of the vehicle, thereby increasing fuel consumption. An
underinflated tire can seriously damage the tire, which could lead to a
blow out and accident. Too much tire pressure, or overinflation, can lead to
excessive tire wear. An extremely over-inflated tire can also lead to a
possible blow out and an accident. Automotive manufacturers label each
vehicle with the recommended inflation pressures for the front and rear
tires.
BRAKE SYSTEMS
Of all the systems on a car, the most important may well be the brake
system. It is one thing to not be able to move forward; it is another thing
again to not be able to stop.
Components
The major components found in any brake system include the following:
Brake pedal: the mechanical connection between the driver’s foot and
the master cylinder.
Master cylinder: located in the engine compartment just in front of the
driver, the master cylinder generates the fluid pressure to operate the
brake assemblies at the wheels.
Fluid reservoir: provides fluid to the brake circuits. The fluid reservoir is
located on top of the master cylinder.
Brake lines: transmit fluid pressure from the master cylinder to the
brake assemblies. These can be steel lines that run along the vehicle
chassis or flex hoses that are used to connect the steel lines to the brake
assemblies.
Assemblies
Brakes work by converting the energy of the vehicle’s motion into heat
energy through friction. The two major types of brake assemblies are as
follows:
Drum brakes: expanding shoes make contact with a rotating drum to
create friction.
Disc brakes: brake pads on either side of a rotating disc are “pinched”
together to slow the vehicle.
Brake systems are hydraulically operated. A pumping piston, located in
the master cylinder, is operated by the brake pedal and puts pressure on
the system’s brake fluid. Since fluids cannot be compressed, the brake
fluid travels through the brake lines and moves the pistons in the brake
assemblies to operate the brakes. The harder the driver presses on the
brake pedal, the more fluid pressure is developed and more braking power
is generated.
Dual Hydraulic Brake Systems
Drum brakes
The parts that develop the friction in a drum brake are the brake shoes.
There are two brake shoes in any drum brake assembly. As hydraulic
pressure is applied to the wheel cylinder, which is located between the
brake shoes, the pistons inside it push apart and act against them. The
brake shoes then push outward against the inner surface of the brake
drum, and the resulting friction between the brake shoes and the brake
drum slows the vehicle.
Disc brakes
Disc brakes are much more powerful than drum brakes because of disc
brakes’ superior ability to reject heat energy. The pistons used to actuate
disc brakes are much larger, and can apply more force to the brake pads.
Also, brake rotors used in disc brakes are more easily cooled, as they are
better exposed to the cool air under the car and are o en designed with air
passages through them to enhance heat rejection.
The piston that operates a disc brake is housed in a brake caliper. This
caliper “floats” laterally as the brake is applied and released, and makes it
possible for one piston to operate the pads on both sides of the rotor. This
makes the caliper operate similar to a C-clamp. As the screw is tightened
on one side, the entire assembly is drawn together and pinches tightly on
the item being clamped; in this case, the brake rotor.
Power brakes
Braking pressure is usually boosted using a brake booster. The brake
booster is located between the brake pedal and the master cylinder.
Engine intake manifold vacuum is utilized to generate greater force on the
master cylinder, so higher hydraulic pressures can be generated in the
brake system for the same amount of pedal force provided by the driver.
Some brake booster systems use fluid pressure from the power steering
system to increase braking power.
Antilock brakes
As in every other vehicle system, computer control is being incorporated
into the brake system. Most cars now come equipped with antilock brakes
(ABS), which prevent wheel lock under hard braking conditions. The ABS
system uses speed sensors attached to each wheel to tell a computer (the
ABS computer) the relative speeds of each wheel. If the ABS computer
detects a difference in wheel speed more than a preset amount, the
computer uses pumps and valves in the ABS system to adjust the brake
pressure for the affected wheel or wheels. This gives more control to the
driver in slippery conditions and allows the vehicle to stop more
predictably and safely.
Let’s see how the test maker will assess your understanding of the chassis
system, and what process you should use to address the question and pick
up the points.
Question
Virtually all modern automatic
transmissions are controlled by
Analysis
Step 1: This question asks you to
recall what component controls
almost all modern automatic
transmissions.
Step 2: There isn’t much
information to simplify here.
Step 3: Virtually all modern
automatic transmissions are
controlled electronically by the
vehicle’s powertrain control
module (PCM).
Question
(A)
(B)
(C)
(D)
the driver
oil pressure
the PCM
the engine
Analysis
Step 4: Answer choice (C)
matches the prediction.
Now try a similar question on your own.
Brakes slow a vehicle by converting motion energy
into
energy.
(A)
(B)
(C)
(D)
sound
electrical
fluid
heat
Explanation
The correct answer is (D). Brakes convert a vehicle’s motion energy into
heat energy through friction.
Auto Information Practice Set 1
Select the best answer for each question. This question set has 10
practice questions, which is the number of Auto Information
questions you will see if you take the CAT-ASVAB.
1. How many revolutions of the cranksha does it take to complete
one cycle of events in a four-stroke cycle engine?
(A)
(B)
(C)
(D)
one-half
one
two
four
2. This image depicts what stroke in the four-stroke cycle?
(A)
(B)
(C)
(D)
intake stroke
compression stroke
power stroke
exhaust stroke
3. A 12:1 air-fuel mixture would be a
(A) rich
(B) lean
(C) stoichiometric
(D) none of the above
4. Diesel engines utilize a
mixture.
(A) high compression ratio
(B) spark ignition system
(C) low compression ratio
(D) carburetor
5. The antifreeze in the engine’s coolant will
(A) lower the boiling point of the coolant
(B) raise the boiling point of the coolant
(C) raise the freezing point of the coolant
(D) lower the corrosion resistance of the coolant
6. Identify this engine component.
(A) spark plug
(B) fuel injector
(C) wrist pin
(D) valve spring
7. Electronic fuel injectors are controlled by the
(A) powertrain control module
(B) fuel pressure regulator
(C) electric fuel pump
(D) ignition switch
8. Where does combustion take place in the engine?
(A) 1
(B) 2
(C) 3
(D) 4
9. The PCM receives signals from the vehicle’s
(A) sensors
(B) diagnostic data link
(C) actuators
(D) scan tool
10. Oil galleries in the crank sha provide pressurized oil to
(A) the pistons
(B) the push rods
(C) the valves
(D) the connecting rod bearings
Auto Information Practice Set 2
Select the best answer for each question. This question set has 10
practice questions, which is the number of Auto Information
questions you will see if you take the CAT-ASVAB.
11. How do shock absorbers dissipate suspension system energy?
(A) by converting motion energy into electric power
(B) by converting motion energy into potential energy
(C) by converting motion energy into heat energy
(D) by neutralizing chemical energy
12. The water-cooled engine component that rejects heat is the
(A) water pump
(B) thermostat
(C) radiator
(D) antifreeze
13. Multiport fuel injectors are located in
(A) the throttle body
(B) the combustion chamber
(C) the intake manifold
(D) the flame front
14. Which of the following is developed in the catalytic converter?
(A) toxic gas
(B) high heat
(C) hydrocarbon gas
(D) carbon trioxide
15. Coil-on-plug ignition systems eliminate the need for
(A) secondary coil winding
(B) spark plug wires
(C) spark plugs
(D) primary coil winding
16. The main component of an engine's charging system is the
____________.
(A) power charger
(B) battery
(C) rectifier
(D) alternator
17. Automatic transmissions do not require a clutch because a
__________ transmits power from the engine to the transmission.
(A) half-sha
(B) torque converter
(C) drive axle
(D) constant-velocity joint
18. Rack and pinion gears are found in which of the following
applications?
(A) steering system
(B) manual transmission
(C) lubrication system
(D) automatic transmission
19. The most important property that enables a hydraulic brake system
to transmit pressure from the master cylinder to all individual
brakes is __________.
(A) viscosity
(B) incompressibility
(C) acidity
(D) adaptability
20. Which of the following is the least expensive and most effective
maintenance procedure to maintain maximum engine life?
(A) lubricating all fittings
(B) regularly changing automatic transmission fluid
(C) regularly changing the oil and filter
(D) properly maintaining the thermostat
Answers and Explanations
AUTO INFORMATION PRACTICE SET 1
1. C
It takes two revolutions of the cranksha to complete each four-stroke
cycle.
2. C
This image depicts the power stroke, which is the third stroke in the
four-stroke cycle. The power stroke generates the engine’s power.
3. A
A 12:1 ratio of air to fuel would be a rich mixture, fast-burning and
possibly producing black smoke.
4. A
Diesel engines operate with a high compression ratio. The compression
ratio for a diesel engine can range anywhere from 16:1 to 22:1.
5. B
Antifreeze raises the boiling point of your coolant, thereby rendering it
much more efficient at transferring heat.
6. A
This is a spark plug. Spark plugs are threaded into the cylinder head,
where they protrude into the combustion chamber and generate the
spark to initiate combustion.
7. A
Of the items given, only the powertrain control module is in charge of
firing and regulating electronic fuel injectors.
8. B
The combustion chamber, indicated in the diagram by the number 2, is
where the actual combustion of the air-fuel mixture takes place. It is
located in the cylinder head directly above the piston (1 in the diagram).
9. A
As the “brain” of the car, it is the job of the PCM to gather signals from
the car’s sensors and generate outputs to control the vehicle’s functions.
The diagnostic data link, choice (B), connects a scan tool to the PCM; the
scan tool, (D), is what technicians use to read the PCM.
10. D
The oil galleries are drilled directly through the crank sha in order to
provide pressurized oil to the connecting rod bearings. The pistons,
push rods, and valves do not receive pressurized oil from the crank sha
oil galleries, so (A), (B), and (C) are incorrect.
AUTO INFORMATION PRACTICE SET 2
11. C
The shock absorber provides damping to the suspension system. The
damping effect converts motion energy into heat, which is then
dissipated though the shock absorber body into the atmosphere. The
shock absorber does not generate electrical power or potential energy,
or neutralize chemical energy. Therefore, choices (A), (B), and (D) are
incorrect.
12. C
The radiator is the engine component designed to reject heat in a watercooled engine. The other answer choices are incorrect because
antifreeze is a subcomponent of the coolant, the water pump circulates
the coolant, and the thermostat regulates the coolant temperature.
13. C
Throttle body fuel injectors are located in the throttle body, so (A) is
incorrect. Direct injection fuel injectors are located in the combustion
chamber, so (B) is incorrect. The flame front is the burning portion of the
fuel air mixture in the combustion chamber, so (D) is incorrect. Multiport
fuel injectors are located in the intake manifold, so (C) is correct.
14. B
The function of the catalytic converter is to further reduce unburned
hydrocarbon fuel in the exhaust gas by decomposing the unburned
hydrocarbon fuel in the exhaust gas into carbon dioxide, water vapor,
and heat. As a result, high heat is developed in the catalytic converter.
Answer choices (A), (C), and (D) are incorrect because they represent
components not developed in the catalytic converter.
15. B
Coil-on-plug ignition systems eliminate the need for spark plug wires
because the ignition coil is mounted directly over the spark plugs.
Answer choices (A), (C), and (D) are still necessary components in a coilon-plug ignition system, and therefore are not correct.
16. D
The alternator converts mechanical energy into electrical energy
needed to operate the vehicle's systems and to charge the battery as
required. Power charger, (A), is a generic term, not a specific
component. The battery, (B), stores electrical energy and the rectifier,
(C), converts alternating current from the alternator to direct current.
17. B
A torque converter converts the rotational power of the engine to fluid
power. A half-sha , (A), connects the transaxle to the drive wheels in a
front wheel drive vehicle. The drive axle, (C), sends power from the
differential to the drive wheels. Constant-velocity joints, (D), are located
between the transaxle and front drive wheels.
18. A
Rack and pinion gears convert rotational motion from the steering
wheel to the linear motion needed to change the direction of the
wheels. This type of gear arrangement is not used in any of the other
systems listed.
19. B
If brake fluid were compressible, the fluid displacement created by the
master cylinder would be diminished at the individual brake piston
assemblies and braking power would be severely diminished. Viscosity,
(A), refers to how easily a fluid flows. While this could have some effect
on brake performance, it is not the most important property. Acidity, (C),
is irrelevant to transmitting pressure and fluid movement. Adaptability,
(D), is not a relevant property.
20. C
Proper lubrication of internal moving parts is essential to long engine
life. Excessive wear on internal engine parts can occur when the engine
oil becomes dirty or experiences degradation of its lubricating
properties. Internal combustion engines are lubricated by circulating oil
internally, not by lubricating fittings, (A). Changing automatic
transmission fluid, (B), does not need to be done frequently and is
important to the life of the transmission more than the engine.
Thermostats, (D), generally don't require maintenance; if they fail to
function properly they are usually replaced.
REVIEW AND REFLECT
Look back over your work on the practice questions. If you got some
questions wrong, think about why.
Are there specific systems you need to review? If so, review this chapter,
and then try to draw diagrams of those systems on your own.
Did you get tripped up over the names of parts? If so, review the chapter,
focusing on the words in bold. Also, consider making those words into
flashcards.
How did you do overall? Do you need to review this chapter
comprehensively?
Want more practice with Automotive Information? Log in at
kaptest.com/login to try more questions in the Qbank.
CHAPTER 12
SHOP INFORMATION
KNOW WHAT TO EXPECT
In order to work effectively in any industrial or technical environment, a
technician must be able to identify tools correctly and use them safely.
Hand tools are the foundation of industry; very little work would get done
without them. Even the largest and most complex piece of equipment
would not run for very long if hand tools were not available for its
maintenance and repair.
The ASVAB Shop Information (SI) test will assess your familiarity with
common tools and their uses. You are given 6 minutes to answer 10 Shop
Information questions on the CAT-ASVAB. On the paper-and-pencil test, the
Auto Information and Shop Information subtests are combined into one,
with 11 minutes to answer 25 questions about both topics.
Measuring Tools
Learning Objectives
In this section, you will learn to:
identify tools used to measure distances
determine when a micrometer is needed
understand the use of calipers
differentiate between types of spirit levels
determine the use of a steel square
A critical skill for any technician is the ability to make accurate
measurements.
TAPE MEASURES AND STEEL RULES
A steel rule or a tape measure can be used to determine distances. These
measure in fractions of an inch as low as
, but are ineffective when
more accuracy is required. This is because the scale becomes too difficult
to read with smaller measurements. Steel rules are also useful for the
layout of straight lines.
Steel Rule
MICROMETERS
When accuracy to the thousandths of an inch is required, a micrometer is
used. The most common type of micrometer is the outside micrometer.
The outside micrometer is made to measure the thickness of flat objects or
the outside diameter of cylindrically shaped objects. It is built similarly to a
C-clamp (see the discussion of C-clamps later in this chapter). The spindle
of the micrometer is rotated in and out to adjust the distance between it
and the anvil. All measurements are taken between the opposing faces of
the spindle and the anvil.
Outside Micrometer
The thimble of the micrometer is attached directly to the spindle. The
sleeve of the micrometer is stationary, and has markings on it indicating
how far the spindle has been moved relative to the anvil. As the thimble
moves outward, it uncovers the graduations on the sleeve. The position of
the thimble relative to the sleeve is what reveals the micrometer reading.
Forty turns of the thimble will move the spindle exactly 1 inch. This means
that each turn of the thimble moves the spindle
" or 0.025". The
graduations on the sleeve are also marked every 0.025" to keep track of
how many times the thimble has been turned. Each time the thimble
completes one turn, another mark on the sleeve is uncovered. Four
complete turns of the thimble move the spindle
of an inch or 0.100", so
this is marked with a large “1” on the sleeve. The mark at 0.200" is a “2,”
and so on.
The outside of the thimble has 25 evenly spaced graduations on it. Since a
full turn of the thimble moves the spindle 0.025", this means that one of
the graduations on the thimble is the equivalent of 0.001". Reading a
micrometer is simply a matter of adding the measurement on the sleeve to
the number on the thimble that aligns with the longitudinal line on the
sleeve.
Example of Reading a Micrometer
CALIPERS
A caliper is a two-legged instrument that is used to measure the distance
between two sides of an object. It can also be used to transfer a
measurement from one object to another. Calipers that measure the
external size of an object are called outside calipers, while those that
measure the internal size of an object are called inside calipers.
Outside Caliper
Inside Caliper
SPIRIT LEVELS
A spirit level is used to determine whether a surface is horizontal (level) or
vertical (plumb). Spirit levels are also known as bubble levels or just
levels. A tubular spirit level is a fluid-filled tube containing a bubble that
is centered when level.
Tubular Spirit Level
A bullseye spirit level is a fluid-filled circle with a slightly convex face,
containing a bubble that is centered when level. While a tubular spirit level
only levels in the direction of the tube, a bullseye spirit level can level a
surface across a plane.
Bullseye Spirit Level
STEEL SQUARES
A steel square is used to measure or lay out angles. A steel square is also
known as a carpenter’s square or framing square, because carpenters
commonly use it to frame stairs and ra ers. Its two arms meet at a 90degree angle. The long arm is known as the blade (or body) and the short
arm is known as the tongue.
Steel Square
Questions on the ASVAB may ask you to choose the most appropriate tool
for a job. Look at this example:
Question
Analysis
Question
Analysis
You need to measure the length
Step 1: This question asks which
of a piece of wood within
tool would be best for measuring
".
Which of the following would be
distance within
".
the best tool to select for this
job?
Step 2: There is nothing to
simplify.
Step 3: You can narrow your
prediction to tools used for
measuring distance. In particular,
the tool must be capable of
making very accurate
measurements of distance.
(A) steel rule
Step 4: Choice (C) matches that
(B) measuring tape
(C) micrometer
prediction. Choice (D) can be
eliminated because it is not used
(D) spirit level
to measure distance, and choices
(A) and (B) can be eliminated
because they cannot perform
measurements of distance below
".
Now give this one a try on your own:
You want to be sure that the joint you are installing is
at a flush right angle. Which of the following tools
could be used for that?
(A) steel rule
(B) spirit level
(C) steel square
(D) caliper
Explanation
The key term here is “right angle.” The only one of these instruments that
allows you to measure a right angle is a steel square, choice (C).
Striking Tools
Learning Objectives
In this section, you will learn to:
differentiate types of hammers and their uses
understand the use of nails
understand rivets and the tools used to install them
identify how punches are used
determine when a dri is needed
HAMMERS
Striking objects in order to remove or install them is the job of the
hammer. Almost every technician uses a hammer of some kind, whether it
is used to drive a nail or to loosen pieces of an assembly. Hammers come in
many designs and sizes according to their intended use.
The type most o en used by metal workers and mechanics is known as a
ball-peen hammer. This hammer is designed with a regular striking face,
like most hammers, but also has a rounded end that can be used for
shaping metal and making gaskets.
Ball-Peen Hammer
Mechanics will o en use a rubber mallet to prevent damage to the parts
they are striking. Rubber mallets are not made for maximum impact; they
are designed to install or remove delicate parts such as hub caps while
preventing damage to their surface. A carpenter would use a wooden
mallet to achieve the same effect.
Carpenters o en will use a claw hammer, which serves a dual purpose.
The hammer head has two ends; one to drive nails and the other to remove
nails. Claw hammers come in a variety of sizes, and these are determined
by the weight of the hammer head. A general-purpose claw hammer would
have a 13 oz head, while a rough-framing hammer, typically used for
framing wooden houses, might be anywhere from 16 to 20 oz.
Claw Hammer
Heavy jobs, such as driving fence posts or breaking down drywall, require
the use of a sledge hammer. This is a long-handle hammer with a large
steel head that typically requires both hands to operate.
Sledge Hammer
NAILS
A nail is a pin-shaped fastener made of metal. One end of the nail comes to
a sharp point, while the other end usually has a flat head. However, there
are also headless nails. The length of the nail body between the head and
point is called the shank. Nails are typically driven into wood by a hammer
or pneumatic nail gun.
Nail
RIVETS
Rivets are metal fasteners that can be used to assemble parts. A rivet is
simply a pin with a head at one end. A rivet is installed in a hole (the same
diameter as the rivet) that is drilled through two pieces that are to be
assembled. With the two pieces tightly clamped, the head of the rivet is
placed on a hard surface, while the other end is formed into a head using a
hammer or special riveting tool. This creates an assembly that is
semipermanent, as the rivet must be drilled out to remove it.
Installation of a Regular Rivet
CHISELS, PUNCHES, AND DRIFTS
Hammers are o en used in conjunction with a chisel, a punch, or a dri . A
chisel normally has a long, sharp edge and is used for cutting. A punch is
narrow and is used for driving small fasteners and making layout marks. A
dri is used for striking an object where it is important that the hammer
itself not come in direct contact with the work.
The most common chisel is the cold chisel, which has a straight, sharp
edge for cutting off bolt heads or separating two pieces of an assembly.
Cold chisels get dull from time to time and must be sharpened on a bench
grinder.
Punches are made in a number of different designs, but the most common
ones are the pin punch and the center punch. Pin punches are straight
and cylindrical in shape. Pin punches come in various sizes, normally
starting as small as
" and going up to
" in diameter. The pin punch is
used to drive pins out of holes, and to follow the pin through the hole as it
forces the pin out.
Pin Punch
Center punches are used to make small indentations that serve as starting
marks for drilling operations. Making a small indentation with a center
punch can help the drill bit stay on target long enough to get a hole started.
Attempting to drill a hole in metal without first marking it with a center
punch can allow the drill bit to “walk” across the work and completely miss
the original target.
Center Punch
When using a hammer to drive parts in or out of an assembly, it is easy to
damage the parts if they are struck directly by the hammer. The head of a
ball-peen hammer is made from forged steel, and thus can easily damage
parts that are made from so er materials. Placing a dri against the object
and then striking the dri with a hammer prevents damage to the part that
is being driven. Dri s are o en made from so metals such as mild steel,
brass, and even aluminum.
Brass Dri
Here is a sample ASVAB question that asks you to differentiate between
striking tools:
Question
Analysis
Question
Analysis
Which of the following hammers
Step 1: This question asks which
would be most appropriate to
hammer would be most
install a hubcap?
appropriate to install a delicate
part.
Step 2: Not much info to simplify.
Step 3: You can narrow your
prediction to hammers best used
for delicate jobs like installing a
hubcap.
(A) claw hammer
Step 4: Choice (D) matches that
(B) pneumatic hammer
prediction. Choices (A) and (C)
(C) ball-peen hammer
(D) rubber mallet
can be eliminated, because their
striking heads are too hard.
Choice (B) can be eliminated
because it exerts too much force.
Now try one on your own.
You hammered a nail into the wrong part of a board
and you want to remove it. With which of the following
hammers could you do that?
(A) ball-peen hammer
(B) wooden mallet
(C) rubber mallet
(D) claw hammer
Explanation
Choices (A), (B), and (C) do not contain any device that could remove a nail.
However, the claw on a claw hammer, (D), is designed especially to remove
nails. That is the tool you would need.
Turning Tools
Learning Objectives
In this section, you will learn to:
identify different types of screwdrivers and their coordinating
fasteners
distinguish between different types of wrenches and the benefits
of each
understand how wrenches and sockets are sized
describe what type of wrench to use for a particular project
understand the concept of torque as it applies to hand tools
understand when and why nuts are used
identify the types of fasteners used with wrenches
understand the system of labeling common fasteners
SCREWDRIVERS
Screwdrivers, which come in many different sizes and styles, are one of the
most common tools used to install and remove fasteners. The oldest
screwdriver design is the flat tip type, which is basically a flat blade made
to turn a screw with a single slot across the top of it.
Flat Tip Screwdriver
The flat tip screwdriver is far less popular now in light of some newer
designs, including the Phillips, Robertson, and Torx screwdrivers. A
Phillips screwdriver is recognizable by its tip that looks like a plus sign.
Robertson screwdrivers have a square tip, and Torx screwdrivers have a
characteristic six-pointed star-shaped tip. All of these newer designs grip
the fastener, making the screw easier to remove and install. Since the
screwdriver makes better contact with the screw, it is also possible to
fasten it more tightly.
Screwdrivers are used with only one type of fastener—screws, which are
threaded fasteners that vary in size and shape depending on the project.
The threads on screws are designed to tighten when turned clockwise.
Read more about how fasteners are classified later in this chapter in the
“Nuts and Bolts” section. Washers, disk-shaped rings, may be used
alongside screws to protect the work surface and distribute the force
caused by tightening the screw.
WRENCHES
With all wrenches, the longer the wrench, the more leverage and the more
twisting force (torque) it can apply to tighten or loosen a fastener. There
are two basic types of wrenches; the open-end and the box-end. The
open-end wrench is made for speed. Since the end is open, it is easy to
slide the wrench on and off a fastener, such as a cap screw. To loosen tight
fasteners, it is a good idea to use a box-end wrench. The box end wraps
completely around the head of a bolt, and therefore makes greater surface
contact, distributing the force more evenly.
The most common wrench arrangement is the combination wrench. This
design has an open end and a box end on opposite ends of a wrench. Both
ends are made to fit the same size fastener, but the technician can loosen
the bolt with the box end, and then finish removing the bolt more quickly
using the open end.
When the specific size wrench for a fastener is not available, an adjustable
wrench (sometimes referred to as a wrenches Crescent® wrench) can be
used.
Adjustable Wrench
SOCKETS
An alternative to using wrenches to loosen fasteners is the use of sockets.
Like wrenches, sockets come in two designs. Six-point is a stronger design
because of its greater wall thickness, and is usually the mechanic’s first
choice in the smaller socket drive sizes. However, twelve-point is a useful
design for certain applications, as it is easier to align with the bolt head in
tight spaces.
Six-Point and Twelve-Point Sockets
To determine the size of a socket required for a job, simply measure the
distance between two parallel sides of the bolt head. If the bolt head
measures
" across two parallel sides, then a
" socket is required to
loosen it.
Sockets come in a variety of drive sizes, which are determined by the size
of the opening that attaches to the drive tool. For instance, if the square
end of a socket measures
" across, then that would be a
The most popular drive sizes are
",
",
", and
" drive socket.
". Larger drive sizes are
available for the very large fasteners used in heavy industry. Take a look at
the diagram below.
Common Socket Drive Size Range
Sockets are very versatile, because they can be used with a variety of drive
tools. The most common drive tool for sockets is the ratchet, which turns
the fastener in only one direction as the handle is moved back and forth
through a narrow arc. Ratchets are reversible, so they can be set to tighten
or loosen a fastener. They can also be more useful than open-end/box-end
wrenches in tight quarters (especially when paired with an extension bar)
because you do not need to replace the tool with each turn—just move the
handle back and forth.
Ratchet
Sockets can also be used with pneumatic (compressed air) power tools,
such as an air impact wrench. The air impact wrench can remove
fasteners quickly by applying tremendous amounts of torque (twisting
force) and using a hammering action that vibrates fasteners loose. It is
important to remember that only impact sockets should be used with an
air impact wrench.
Air Wrench
NUTS AND BOLTS
Some of the most common types of tools to be tested on the ASVAB are
fasteners (screws and bolts). It pays to review this wide range of hardware.
Wrenches of all types are used with a variety of threaded fasteners called
bolts and nuts. A bolt has external threads, whereas a nut has internal
threads. Bolts typically have a hexagonal or square head, which is held in
place with a wrench while the nut is tightened (also with a wrench) to
fasten the assembly. A threaded bolt can only be inserted into a nut or hole
that has a similar thread.
While there is not a clear-cut distinction between screws and bolts, the
most practical way to distinguish between the two is based upon the shape
of the head and what tool is used to install or remove the fastener. While
bolts have a hexagonal (six-sided) or square head and are used with a
wrench and nut, screws typically have a round head with an indentation
that matches the screwdriver that must be used to install or remove the
screw. Both fasteners are threaded on part or all of the sha .
Nuts thread onto bolts to clamp assemblies together. Nuts usually have
either a square head or a hexagonal head, and can be locked into position
using several different methods.
Wing nuts make it possible to disassemble a component by hand. The two
“wings” attached to the nut make it easy to tighten and loosen without the
aid of hand tools.
Wing Nut
A castellated nut uses a cotter pin to lock it into place. The cotter pin
passes through a hole in the bolt or stud that the nut is threaded on,
engaging the cutouts in the nut.
Lock nuts have a nylon insert incorporated into its threads that provides
enough interference to prevent the nut from loosening, thus locking it in
place.
Lock Nuts
The type of thread that is placed on a fastener will vary according to the
diameter of the fastener and the intended strength of the finished product.
Threads are identified by their pitch, and this is measured using a thread
pitch gauge.
Fractional-measurement fasteners (measured in fractions of inches) use
threads that are identified by the number of threads per inch. There are
two basic thread classifications within this group: Unified National Coarse
(UNC), and Unified National Fine (UNF). A UNC or coarse thread would
have relatively few threads per inch, where a UNF or fine thread would
have a larger number of threads per inch.
A bolt that is
" in diameter could, therefore, have two possible thread
pitches. If it were a UNC bolt, it would have 16 threads per inch, whereas if
it were a UNF bolt, it would have 24 threads per inch.
Bolt Designation Numbers
Two other important measurements of a fastener include the diameter
and the length. The diameter is the distance across the unthreaded
portion of the bolt. This would give an indication of the size of hole that the
fastener is made to be installed in. The length of the bolt is the distance
between the underside of the bolt head and the end of the bolt. Note that
the bolt head does not count toward the length of the bolt.
Fastener Diameter and Length
Let’s check out one way fasteners could be tested on the ASVAB:
Question
Analysis
You are assembling a project with
bolts that you would like to be
able to remove later, even if you
Step 1: You’re asked to
determine the best type of nut to
use in the given project.
do not have a wrench with you.
What would be the best type of
Step 2: The key phrase is “even if
nut to use in this assembly?
you do not have a wrench with
you.” Think about what type of
nut can be removed easily with
just your hands.
Step 3: Make a prediction: a wing
nut can be removed using only
your hands.
(A) lock nut
Step 4: Choose answer (C).
(B) standard nut
(C) wing nut
(D) castellated nut
A Test Day question may ask you about the correct size tool to use. Take a
look at this question:
You have a bolt that needs to be removed, but an
"
open-end wrench is just slightly too big to fit properly.
Which of the following sizes should be tried next?
(A)
"
(B)
"
(C)
"
(D)
"
Explanation
The key phrase to focus on in this question is that the
" wrench is just
slightly too big. So, you are looking for a wrench that is a bit smaller. It can
be tricky to tell which fraction is smaller, but a quick way to do that is to
find a common denominator for each fraction. (Review the fraction rules in
chapter 6: Arithmetic Reasoning if you need a quick reminder.) Convert all
the fractions to have 16 as the denominator so they are easier to compare.
Choice (A) is larger than ", so that can be eliminated right away. Choices
(C) and (D) are significantly smaller than
", so they also do not fit what
we are looking for. Choice (B), on the other hand, is the size of a wrench
just smaller than an
answer.
" wrench (
" is equal to
"), so that is the correct
Fastening Tools
Learning Objectives
In this section, you will learn to:
identify where and why snap rings are used
differentiate ways to join metals
determine when and how to solder
determine when and how to weld
RING FASTENERS
Retaining rings (or snap rings) are used to prevent end-movement of
cylindrical parts in bores or parts mounted on sha s. External snap rings
are installed in grooves on sha s, whereas internal snap rings install in
grooves inside a bore. Snap rings are installed and removed using snapring pliers.
Internal Snap Rings and External Snap Rings
SOLDERING TOOLS
Soldering is a process that joins metals by bonding a metal alloy to their
surfaces. It is a low-temperature process that can be performed with
simple tools and inexpensive materials.
Most solder is an alloy of lead and tin. The percentages of each metal in the
solder will vary depending on the desired properties of the solder, e.g., its
melting point. Higher percentages of lead will result in a lower melting
point.
The most critical part of soldering is the cleaning of the surfaces to be
joined. Any oxides or other contaminants on the surface to be soldered will
prevent a solid connection from being made. The best way to prepare a
surface for soldering is to use a flux that will clean the surfaces with a
chemical action. Electrical connections require a rosin flux, and solders
made for this will have the flux contained in the core of the solder. This is
known as rosin-core solder.
There are a number of tools that can be used to generate the necessary
heat to melt the solder, but in most cases a soldering iron is used. Most
soldering irons are electrically powered, and can draw anywhere from 25
to 100 watts. Low-power irons would be used to solder electrical
connections, whereas higher powered ones would be used in sheet metal
work.
Soldering Iron
A tool that is o en used for soldering electrical connections is the
soldering gun. A soldering gun has a two-step trigger that allows the
technician to quickly select a low or high heat setting. The main advantage
to a soldering gun is the very rapid warm-up cycle. A soldering gun also has
a light built into it for illuminating the work.
Soldering Gun
When soldering, start by mechanically cleaning the materials to be joined.
This may involve the use of a stainless steel brush or even sandpaper. Heat
the surfaces gently while applying flux to them, and then add solder once
the flux has thoroughly cleaned the material. Tin the surfaces by spreading
the solder thinly over the surface, making sure to thoroughly heat any area
that is to be tinned.
Before soldering an electrical connection, it is always a good idea to make
a solid mechanical connection first. This will involve stripping insulation
from wires and twisting them together. Keep in mind that the entire
connection needs to be heated before applying solder to it. If only the
solder is heated and it then is “melted” onto relatively cool wires, a ““cold”
solder joint is created that can exhibit unusual electrical properties.
WELDING TOOLS
When joining metals, the best way to achieve a high-strength joint is to use
a welding process. Welding is very different from soldering in that it
involves melting the base metal of the objects to be joined, a process that
requires very high temperatures.
There are two major types of welding processes: oxyacetylene welding
and electric-arc welding. Oxyacetylene welding involves the use of a torch
that is fueled with oxygen and acetylene. Burning these two gases together
creates an extremely hot flame, hot enough to melt steel and other ferrous
(iron-based) materials. Filler rod is melted along with the base metal to
produce a finished weld.
There are many specialized processes that fall under the electric-arc
welding classification. The simplest and most easily recognized type is
known as stick welding. Stick welding involves the use of an electric-arc
welding machine and two cables: one that attaches to the work being
welded through a ground clamp, and the other going to an electrode that
is sometimes referred to as a stinger. The stinger is held by the welder and
is used to hold the welding rod.
Stick Welder
When the welder touches the welding rod on the work piece, an electric arc
is formed. This electric arc generates a tremendous amount of heat and
accomplishes three things. First, the heat melts the base metal of the
material being welded. Second, the heat melts the electrode and deposits
this metal in the weld as filler. Lastly, the flux on the outside of the
electrodes burns and the generated gases form a “shield” around the weld.
This gaseous shield prevents air from reacting with the hot metal and
therefore weakening the weld.
As the welder continues the weld, the electrode burns and becomes
shorter. The means that the welder must continue moving the stinger
closer to the work until the electrode has been consumed. Once the
electrode is used up, the welder breaks off or stops the arc, and a new
electrode is placed in the stinger to continue the weld.
If more heat is needed to perform the weld, the welder can increase the
amount of electric current that is supplied by the welding machine.
Generally speaking, the larger the pieces that are being welded or the
larger the electrode that is being used, the greater the amount of current
required to get the weld done.
The electric arc that is generated during this process gives off a very high
intensity light. The ultraviolet light is so intense that it can “sunburn”
exposed skin and burn the retinas of unprotected eyes. Welders must,
therefore, cover all exposed skin with protective clothing (preferably
leather) and wear face shields (helmets) with light filters. The filters are
usually very dark, so the welder can view the welding process itself but
nothing else.
Newer welding helmets have electronic filters that sense the ultraviolet
light from an electric arc and switch from clear to shaded in a split second.
This allows the welder to leave the helmet down while lining up the next
weld, saving the time consumed by flipping the helmet up and down.
Another electric-arc welding process that continues to gain popularity is
MIG (metal inert gas) welding. MIG welding is also known as wire-feed
welding because the electrode used for the weld process is a wire that is
automatically fed from a spool. MIG uses a bottled inert gas (such as argon)
to shield the weld, and requires a relatively sophisticated welding
machine.
MIG Gun
Let’s look at an example of how the ASVAB might test your knowledge of
joining metal:
Question
The purpose of flux in metal
joining processes is to
Analysis
Step 1: This question asks what
function flux serves when joining
metal.
Step 2: There is nothing to
simplify.
Step 3: Predict that flux prevents
oxidation by cleaning metal
surfaces.
(A) clean metal surfaces to be
Step 4: Choice (A) matches that
joined
(B) physically bond two metal
surfaces
prediction. Eliminate choice (B),
because although flux is used in
the metal joining process, it is not
(C) transfer electrical current
(D) transfer electrical voltage
the actual bonding agent.
Eliminate choices (C) and (D),
because flux is not intended to
transfer electricity.
Try out another example about fasteners on your own:
Using which of the following tools absolutely requires
the use of a protective face mask?
(A) electric drill
(B) stick welder
(C) ratchet
(D) hand saw
Explanation
Which tool requires the use of a face mask? That would be the stick welder,
(B), which produces high-intensity light that could burn the skin and
retinas if a protective face mask is not used. While it might be a good idea
to wear a protective mask with the other tools, depending on the particular
job, it is not always necessary.
Gripping Tools
Learning Objectives
In this section, you will learn to:
identify the different types of pliers
understand how different types of pliers are used
describe the importance of clamps and vises for carpentry
projects
PLIERS
Repair operations o en call for objects to be gripped, twisted, bent, or
turned. Sometimes these objects are irregularly shaped or otherwise
difficult to hold. The best tool to use for gripping objects like this is pliers.
The most common type of pliers is the combination slip-joint. These are
adjustable at the joint of the two handles of the pliers. With two different
positions to choose from, these pliers can grip objects in a wide range of
sizes. Sometimes, this design also incorporates a wire cutter for increased
versatility.
Combination Slip-Joint Pliers
When large diameter objects must be gripped or twisted, a technician
would use adjustable joint pliers to get the job done. These are adjustable
over a large range of sizes, as they have multiple “arc-joints” that the pliers
can be set into. The handles are also very long, which gives very good
leverage and makes for maximum gripping power. These pliers are also
commonly known as water pump pliers or pliers Channellock® pliers.
Channellock Pliers
Lineman pliers are used for cutting and bending heavy gauge wire. These
are not size-adjustable, but are made for maximum leverage at the jaws to
make the cutting process easier. This type of pliers would most o en be
used by electricians, but all trades utilize them at one time or another.
Lineman Pliers
Diagonal cutters are pliers that are made exclusively for cutting. The two
jaws are set at an angle (diagonally) to make it easier to cut wires straight
across. Diagonal cutters are normally used for cutting wire and small
cables.
Diagonal Cutters
For holding small objects in tight places, a pair of needle nose pliers could
be used. These have very long, pointed jaws for maximum reach. Needle
nose pliers are o en used for intricate jobs like soldering circuit boards and
small components, and they will most o en have a wire cutter built into
them at the base of the jaws.
Needle Nose Pliers
Locking pliers are used by technicians of all trades. Most people know
them as pliers Vise-Grip® pliers. They are adjustable, made in a large
variety of jaw designs, and will lock tightly in place for holding or clamping
objects together. Locking pliers o en have wire cutters built into them as
well for maximum versatility.
Vise-Grip Pliers
Questions on the ASVAB may give you a hypothetical job and ask what tool
would be most useful. Look at this example:
Question
Analysis
Question
Analysis
You are completing a job that
Step 1: This question asks which
requires gripping several
different sizes of pipes. Which of
tool would be best for gripping a
wide range of pipe sizes
the following would be the best
tool to select for this job?
Step 2: There is nothing to
simplify.
Step 3: You can narrow your
prediction to types of pliers, since
that is the tool of choice for jobs
that require gripping. Your
prediction can be even more
specific if you recall that
adjustable joint pliers provide the
most versatility because they can
be adjusted over a wide range of
sizes.
(A) adjustable joint pliers
Step 4: Choice (A) matches that
(B) needle nose pliers
(C) lineman pliers
prediction. Choices (B) and (C)
can be eliminated because they
(D) adjustable wrench
are not adjustable, and choice (D)
can be eliminated because it is
designed for tightening and
removing fasteners rather than
gripping pipes.
Here is another question, this time dealing with terminology. Try this one
on your own:
What type of wrench is commonly known as a Crescent
wrench?
(A) open-end wrench
(B) box-end wrench
(C) adjustable wrench
(D) combination wrench
Explanation
Crescent is such a popular brand that it has become practically
synonymous with the adjustable wrench; (C) is the correct answer.
Remember, a combination wrench has an open-end wrench on one end
and a box-end wrench on the other.
CLAMPS
A clamp is a tool that applies pressure to prevent movement between
different pieces of a project. For example, a clamp would be useful for
holding a project together while glue dries. Consisting of a metal frame
(commonly C-shaped) with a flat-edged screw perpendicular to the bottom
of the frame, a clamp gets tighter as the screw is turned.
C-Clamp
VISES
Vises are similar to clamps in that they are designed to hold wood or other
materials in place. A key difference, however, is that vises are affixed to the
workstation and are used to hold a material in place while you saw, sand,
drill, or otherwise work on the material. Typically, one side (jaw) of the vise
is fixed, and the other is moved by turning a handle.
Vise
Cutting Tools
Learning Objectives
In this section, you will learn to:
identify different types of saws
explain how saw blades differ based on the material they are
designed to cut
select the appropriate hand saw for a particular project
understand the benefits of using powered saws for certain
projects
understand how power drills and their accessories are used
MANUAL (HAND) SAWS
Cutting a material like wood requires the use of a saw. Saws are used in
many different trades, but are typically utilized by carpenters.
The crosscut saw is designed to do what its name suggests: cut across the
grain of the wood. Crosscut saw teeth are unique in that they cut like a
knife. This is in contrast to a rip saw, which is made to cut with the grain of
the wood and whose teeth are shaped like chisels. A rip saw’s teeth are
also set (bent) alternately from side to side to cut a relatively wide kerf
(slot). This style of teeth allows the rip saw to cut a straight line even if the
grain of the wood is curved.
Crosscut Saw
Rip Saw
A coping saw is used to make fine, curving cuts. This saw uses a thin,
flexible blade that is held tight on a wide frame. The blade can be rotated
in the frame for further flexibility, making it easier to make difficult cuts on
larger pieces of material.
Coping Saw
The back saw is also made from thin material, but has a rigid strip of steel
on its top edge for reinforcement. A back saw is normally used for making
fine cuts, so it has 14 to 16 teeth per inch. Back saws can be used with a
miter box for making even cuts at specific angles.
Miter Box and Back Saw
The one saw that can be found in a mechanic’s toolbox is a hacksaw.
Hacksaws are used for cutting metals such as steel, aluminum, or copper.
The blades in a hacksaw are replaceable, and it is important to choose the
right blade for the material that is going to be cut.
Hacksaw
When selecting a hacksaw blade, keep in mind that larger numbers of teeth
per inch help when cutting thinner materials. Also, remember that when
installing a new blade, the blade must be oriented so that the teeth point
away from the handle. This makes the hacksaw cut on the forward stroke,
so let up on the downward pressure when pulling the hacksaw back to
prevent breaking the blade.
POWERED SAWS
For jobs that require faster cuts or that involve especially strong materials,
powered saws may be used in lieu of hand saws. A common type of
powered saw is a circular saw, which—as the name suggests—has a
circular blade that rotates quickly to make a cut. There are two very
common types of circular saw. A miter saw is a self-contained tool that sits
atop a tool bench and is useful for making crosscuts in lumber, especially
when the cut needs to be at a specific angle. Don’t get this confused with a
table saw, which also has a circular blade; a table saw has the blade
actually embedded into the table or bench itself. Another key difference
lies in how the saws are used. To use a miter saw, clamp or otherwise brace
the material to be cut in order to keep it steady, and then lower the rotating
circular saw to make the cut. To use a table saw, carefully slide the material
to be cut toward the rotating blade.
Miter Saw
Another common type of power saw is a band saw, which is so called
because its blade is one continuous band of metal that revolves very
quickly on two spinning wheels to make a continuous cut in a piece of
wood or metal. Band saws are used for creating lumber out of timber and
can also be useful for cutting straight or curved lines in a material. When
using a saw like this for cutting metal, it is vital to use a coolant wash to
keep the material cool and debris-free.
DRILLING AND BORING TOOLS
Making small holes in wood or metal is done by drilling the material. Large
holes can be made in wood or so metals using a process known as
boring. The two processes are essentially the same, but they use different
tools to get the job done.
Drill bits are used for drilling holes. A carpenter would use drill bits up to
" in diameter, but a mechanic would commonly use drill bits as large as
". If holes larger than this must be made, special tools would be used to
bore the hole.
The vast majority of drill bits are made to cut while rotating in a clockwise
direction. These are known as right-hand drill bits. Le -hand drill bits are
made to cut in the opposite direction. The most common practical
application for a le -hand drill bit is the removal of broken bolts from
threaded holes.
Hole saws can also be used for boring large holes. Hole saws are not
adjustable, so each one is only capable of drilling one size of a hole.
Hole Saw
Today, it is rare for anyone to use hand-operated tools to drive drill bits and
other boring tools. Instead, it is common practice to perform these
operations using an electric drill. Electric drills can be identified by chuck
size, reversibility, and whether they are designed to operate at a constant
or variable speed.
The chuck of an electric drill is the part that holds the drill bit. A chuck is
identified by the largest diameter bit that will fit in it. Common chuck sizes
include ", ", and ". Regular drill chucks can be tightened and loosened
using a chuck key. Since it is easy to lose a chuck key, keyless chucks are
becoming more popular. A keyless chuck makes it possible to tighten and
loosen the chuck by hand.
Some drills can operate in both the clockwise and counterclockwise
directions. These are known as reversible drills. Variable speed drills are
designed to operate over a range of speeds that can be determined by the
position of the trigger.
As battery technology advances, it is getting more common for people to
use cordless drills. Longer times between battery recharges and
portability are just two of the reasons why these have become so popular.
Many of these cordless drills come with a wide range of attachments
(called drivers or bits) and can double as powered screwdrivers and socket
wrenches as well.
The most important safety consideration when using a drill is to use a
sharp bit. Dull bits require more time and more pressure placed on the drill
to get the job done. With smaller bits, this could result in bit breakage and
damage to the surface of the material being drilled. Drill bits can be
sharpened on a bench grinder using a special attachment.
Question
Analysis
You are attempting to cut a
rounded shape from a square
Step 1: This question asks which
tool would be best for cutting a
piece of wood. What is the best
round shape from a square.
saw to choose?
Step 2: Not much info to simplify.
Step 3: You can narrow your
prediction by thinking about the
type of saw that can cut a round,
rather than straight, line.
Question
(A) coping saw
(B) crosscut saw
(C) hack saw
Analysis
Step 4: Choice (A) matches that
prediction. The remaining saws
are designed for straight cuts.
(D) rip saw
Now try your hand at a question about saws.
Which of these would a mechanic be most likely to
use?
(A) coping saw
(B) crosscut saw
(C) hacksaw
(D) rip saw
Explanation
Of these four choices, only choice (C), hacksaw, is commonly used to cut
materials other than wood, so that is the saw most likely to be in a
mechanic’s toolbox.
Finishing Tools
Learning Objectives
In this section, you will learn to:
identify tools used to plane, smooth, and shape
determine when and how to use a plane
understand the uses of chisels
determine when to use a file
identify when to use a rasp
PLANES
When working with wood, there are many occasions when it is necessary
to shave off a small amount of material to make a piece fit properly or to
make a surface smooth. One tool that can be used for this purpose is a
plane.
There are several different types of planes, but the one that would be best
suited for general purpose work is the jack plane. The jack plane has a
smooth lower surface (plane bottom) and an adjustable-depth blade that
protrudes slightly below this surface (through the mouth). This blade is set
at an angle, similar to the blade in a disposable razor.
Jack Plane
When using a jack plane, the carpenter grasps the plane with both hands
and moves it evenly across the surface of the work, shaving a thin layer of
wood. If a heavier cut is desired, the blade can be adjusted to protrude
farther from the lower surface of the plane.
WOOD CHISELS
Wood chisels may also be used to shape or smooth a wood surface. Wood
chisels come in a variety of widths, which can range from " to 2". A wood
chisel is normally hand-operated, but when making deep cuts, a so -faced
mallet should be used to lightly tap the chisel through the work.
Wood Chisels
FILES AND RASPS
Files are used to smooth, polish, and shape materials. Files are made from
hardened steel and consist of diagonal rows of teeth. These teeth can be
arranged as either a single row of parallel teeth (single-cut) or one row of
teeth crisscrossing with another row (double-cut). Files are made in flat,
round, half-round, and triangular designs.
Most files do not come with handles. It is important to have a handle ready
to attach to a file when it is put to use, as this will prevent the end of the file
from being driven into the technician’s hand. Remember that a file is made
to cut only on the forward stroke, so it should be li ed slightly from the
work when it is pulled back.
Flat File, Half-Round File, and Triangular File
Rasps are basically very coarse files that are used to trim, shape, and
smooth materials. While files are used for fine finishes, rasps are used for
coarse work. Round rasps are useful for cleaning up holes, whereas a flat
rasp would be used to smooth flat surfaces. The cutting teeth on a rasp are
coarse enough to clear sawdust easily, so the rasp is always ready for the
next stroke.
Rasps
The ASVAB may ask you which tools can be used together on a project.
Here is an example:
Question
Analysis
Question
Analysis
Which of the following finishing
Step 1: This question asks which
tools may be used with a mallet?
tool would be most appropriate
to use with a mallet.
(A) jack plane
(B) wood chisel
Step 2: There is nothing to
(C) file
simplify.
(D) rasp
Step 3: Predict the tool that
would most likely be struck by a
mallet during normal operation.
Step 4: Only choice (B) is
commonly struck by a mallet, to
make deep cuts.
Try this example on your own.
What must be used in conjunction with a file for safe
operation?
(A) mallet
(B) file
(C) chisel
(D) handle
Explanation
The correct answer here is (D), handle. Many files are sold without handles
attached, but it is important to use a handle whenever you use a file, to
prevent the pointed end of the file from injuring the palm of your hand.
Shop Information Practice Set 1
Select the best answer for each question. This practice set has 10
practice questions, which is the number of Shop Information
questions you will see if you take the CAT-ASVAB.
1. In order to tighten a bolt as much as possible, a
wrench should be used.
(A)
(B)
(C)
(D)
long-handled
short-handled
heavy
reticulated
2. What is the tool shown below known as?
(A) water pump pliers only
(B) retaining ring pliers only
(C) Channellock pliers only
(D) both water pump pliers and Channellock pliers
3. A combination wrench has
(A) two different size box ends
(B) two different size open ends
(C) a box end and an open end of the same size
(D) an open end and a ratchet end
4. The blade in a hacksaw should be installed with its teeth pointed
(A) toward the handle only
(B) away from the handle only
(C) either toward or away from the handle
(D) neither toward nor away from the handle
5. How is the length of a bolt measured?
(A) by measuring the length from end to end
(B) by measuring the length of the threaded portion only
(C) by measuring the length from the underside of the head to the
end of the threads
(D) none of the above
6. A bolt with a hexagonal head could be loosened using all of the
following EXCEPT
(A) an open-end wrench
(B) a box-end wrench
(C) a 12-point socket and ratchet
(D) a Torx screwdriver
7.
The tool shown above is used for
(A) installing pop rivets
(B) stapling asphalt shingles
(C) crimping electrical terminals
(D) soldering electrical connections
8. “Tinning” is a process that is related to
(A) carpentry
(B) roofing
(C) soldering
(D) welding
9. The following screw head would be used with which type of
screwdriver?
(A) flat tip
(B) Phillips
(C) Robertson
(D) Torx
10. What force is responsible for allowing wrenches to tighten or
loosen fasteners?
(A) acceleration
(B) torque
(C) tension
(D) friction
Shop Information Practice Set 2
Select the best answer for each question. This practice set has 10
practice questions, which is the number of Shop Information
questions you will see if you take the CAT-ASVAB.
11. The best choice to loosen a tight fastener is the
wrench.
(A) open-end
(B) adjustable
(C) box-end
(D) Allen
12. To determine the correct socket size needed for a given bolt head,
measure the distance between two
of the bolt head.
(A) adjacent sides
(B) parallel threads
(C) opposite points
(D) parallel sides
13. What is a benefit of using a ball-peen hammer rather than a claw
hammer?
(A) It is more suitable for hammering on metal because of its
generally stronger head.
(B) It is more delicate and can thus be used on fragile surfaces.
(C) It can remove nails as well as hammer them in.
(D) It provides more leverage.
14. You have a bolt that needs to be removed, but a
" open-end wrench is just slightly too small to fit properly. Which
of the following sizes should be tried next?
(A)
"
(B)
"
(C)
"
(D)
"
15. What is the most accurate name of the tool shown below?
(A) hole saw
(B) router
(C) borer
(D) smoother
16. Kerry wants to create a jigsaw puzzle by gluing a photograph to a
thin piece of wood and then cutting the laminated picture into
many odd-shaped pieces, which can then be reassembled into the
original picture. Unfortunately, she does not have an electric jigsaw
at her disposal. What would be her best choice of a saw type to
perform this task?
(A) hacksaw
(B) crosscut saw
(C) coping saw
(D) rip saw
17. Dirk wants to cut a piece of thick metal into two smaller pieces
using his hacksaw. Which tool would be best to hold the metal in
place when he cuts?
(A) vise
(B) C-clamp
(C) miter box
(D) adjustable joint pliers
18. Retaining ring fasteners are primarily used to __________.
(A) connect two odd-shaped pieces together
(B) provide a tight seal for a cylinder
(C) suspend gears that don't have sha s attached
(D) prevent end movement of cylindrical parts
19. The part of a nail between the head and the point is called the
__________.
(A) cubit
(B) shank
(C) body
(D) span
20. What is a function of the thimble of an outside micrometer?
(A) to move the spindle so that it touches the object being
measured
(B) to balance the instrument
(C) to move the sleeve into the proper position
(D) to keep the measuring graduations clean
Answers and Explanations
SHOP INFORMATION PRACTICE SET 1
1. A
The tightest connection can be achieved by applying the most torque to
the bolt. Since torque is the product of force and the length of the lever
arm, a long-handled wrench would apply more torque to the bolt than a
short-handled wrench if the same force were applied. Although a heavy
wrench might be a long wrench, the weight of the wrench is not a factor.
Reticulated, meaning resembling a network, is not applicable.
2. D
When large-diameter objects must be gripped or twisted, a technician
would use adjustable joint pliers to get the job done. These are
adjustable over a large range of sizes, as they have multiple “arc-joints”
that the pliers can be set into. The handles are also very long, which
gives very good leverage and makes for maximum gripping power.
These pliers are also commonly known as water pump pliers or
Channellock pliers. Since choice (D) allows for the tools in both choices
(A) and (C), it is the correct answer.
3. C
The box end of a combination wrench is typically used to apply
maximum torque, while the open end is used to turn the fastener more
quickly.
4. B
When installing a new hacksaw blade, orient it so the teeth point away
from the handle. This makes the hacksaw cut on the forward stroke and
also makes it easy to pull the saw back in order to begin the next
forward stroke.
5. C
One important measurement of a fastener is the length. The length of
the bolt is the distance between the underside of the bolt head and the
end of the bolt. Note that the bolt head does not count toward the
length of the bolt. Therefore, the best answer is (C).
6. D
The two basic types of wrenches—the open end and the box end—are
both acceptable for loosening a hexagonal bolt. The open-end wrench is
easy to slide on and off a fastener. The downside to the open-end
wrench is that it only makes contact with two sides of a six-sided (hex)
bolt head. The box-end wraps completely around the head of a bolt, and
therefore makes greater surface contact. Box-end wrenches normally
come in a 12-point configuration, but some are made as 6-point. Used
with a ratchet, the correct size socket is a good choice for loosening
fasteners such as hexagonal bolts. A Torx screwdriver, despite its name,
generally does not exert as much torque as a wrench; it also requires a
bolt that is specially configured to match its shape.
7. D
The tool shown is a soldering gun. It is used for soldering electrical
connections.
8. C
If two pieces to be joined by soldering are large, it may pay to tin the
surfaces before attempting to join them. Heating the surfaces gently
while applying flux to them, and then adding solder once the flux has
thoroughly cleaned the material will accomplish this. Since soldering is
the process involved, the correct answer is (C).
9. C
The Robertson screwdriver grips the fastener better than a flat tip
screwdriver, so the screw is much easier to remove and install.
10. B
Whenever you see the words “force” and “wrench” in the same
sentence, you should immediately think about torque, (B). You can think
of torque as twisting motion, which is exactly what allows a fastener to
be tightened or loosened. Don’t get torque confused with tension, (C),
which instead is a pulling force associated with a weight on a string or
wire.
SHOP INFORMATION PRACTICE SET 2
11. C
The box-end wrench is closed, which allows for more surface area
contact of the wrench with the fastener, compared to the contact offered
by the open-end and adjustable wrenches; therefore, answer choices (A)
and (B) are incorrect. Allen wrenches are typically intended for lowtorque applications; therefore, answer choice (D) is also incorrect.
12. D
The size of a socket for a given bolt head is determined by the distance
between two parallel sides of the bolt head.
13. A
A ball-peen hammer has one main benefit: it generally has a stronger
head made of steel. This matches choice (A). Choice (B) more closely
describes a mallet, certainly not a steel hammer, and choice (C)
describes a benefit of a claw hammer, so that is the opposite of what
you’re looking for. Finally, it makes little sense to talk about (D) leverage
when discussing striking tools.
14. B
If a wrench is just slightly too small, you will want to try the next size
larger. In this case,
" is the next size up. This is the wrench you would
want to try next, so choice (B) is the correct answer.
15. A
The hole saw rotates about its sha and the saw teeth cut a circular hole
perpendicular to the sha . A router, (B), has a single blade that is
typically used to cut a channel or to shape material. Borer, (C), is a
generic term that applies to a variety of tools that can produce holes.
Similarly, smoother, (D), is a catch-all term, and the hole saw shown
would not help to smooth anything.
16. C
A coping saw has a thin blade that can be rotated within its frame in
order to make fine curving cuts. The hacksaw, (A), though similar in
appearance to a coping saw, has a thicker fixed blade and is typically
used for cutting metal. Each of the crosscut saw, (B), and rip saw, (D),
has a large, fixed blade. The crosscut saw is used to cut across the grain
of wood, while the rip saw is used to cut with the grain of wood.
17. A
Since a vise is affixed to a workstation, that tool would hold the metal
stationary while Dirk is cutting and both of his hands would be free. A Cclamp, (B), is better suited for holding two pieces of material together, as
would be required to attach one to the other. A miter box, (C), is typically
used with a back saw to make cuts at specific angles. It would be
difficult, if not impossible, for Dirk to hold the metal stationary with
adjustable joint pliers, (D).
18. D
The protrusions on retaining rings (also called snap rings) fit into
grooves so that they prevent a cylindrical sha from sliding out of
position. Retaining rings do not connect pieces, nor are they ordinarily
used with odd shapes, so (A) is incorrect. They do not provide any type
of seal, so (B) is incorrect. Suspending a gear with no sha , (C), seems to
be a useless function.
19. B
Cubit, (A), is a measurement of length. While body, (C), and span, (D),
may seem to be logical answers, the proper term is shank.
20. A
Turning the thimble moves the spindle into contact with the object
being measured. While the thimble is also used to read the
measurement, it has nothing to do with keeping the graduations clean.
There is no need to “balance” a micrometer to use it. The sleeve
surrounds the spindle and does not move.
REVIEW AND REFLECT
How did you do on this practice set? As you review your work, think about
these questions:
Are there certain categories of tools you should review?
Do you know the names of tools but need more review about when to
use them?
Would it help you to make flashcards out of the bold words in this
chapter?
Want more practice with Shop Information? Log in at kaptest.com/login to
try more questions in the Qbank.
CHAPTER 13
MECHANICAL COMPREHENSION
KNOW WHAT TO EXPECT
In order to understand how machines work, it is important to have a good
grasp of applied physics. The study of applied physics is the study of the
practical application of the laws of physics. Engineering, architecture, and
heavy equipment operation depend upon applied physics. This chapter
will build on concepts first discussed in the Physical Science portion of
chapter 9: General Science to explain how various common mechanical
devices operate.
On the CAT-ASVAB, you will have 22 minutes to answer 15 questions in the
Mechanical Comprehension subtest. If you are taking the paper-and-pencil
test, you will have 19 minutes to answer 25 questions.
A Review of the Physics of
Mechanical Devices
Learning Objectives
In this section, you will learn to:
recognize a mechanical device as any machine based on force
and motion laws
define mass and force
apply Newton’s laws of motion to questions about mechanical
devices
Mechanics is the area of physics that encompasses the laws of motion,
energy, and forces. Velocity, momentum, and Newton’s second law relating
force, mass, and acceleration are all mechanical concepts. All mechanical
devices, including the simple machines discussed in this chapter, are
based on the application of force in order to achieve a movement or
change in position of a mass.
Each of the physical quantities reviewed in this section were first
introduced in the Physical Science section of chapter 9: General Science.
This brief review will focus only on the concepts from that chapter which
most directly underlie mechanical operation.
MASS AND FORCE
All matter has mass. Mass is a measure of the total quantity of matter in an
object. Generally speaking, larger objects tend to have greater mass, but
some materials contain more mass than others per unit volume (are
denser), so bigger doesn’t always mean more massive. Unlike the force of
weight, which will be discussed in more detail a little later in the chapter,
mass is not a vector quantity, since it has magnitude but no direction.
For the purposes of mechanics, the most important thing to know about
mass is that it corresponds to how much force is required to achieve a
particular acceleration. In other words, the more mass something has, the
more difficult it is to change its motion. The term inertia is sometimes
used to refer to an object’s resistance to changes in its motion, but inertia
is just a property of mass.
A force is a push or pull. Forces are everywhere in the world. Some are
fairly obvious, such as a tractor pulling a plow, a baseball being hit into the
stands, or a person shoving his way past others in a crowded store. Other
forces are o en taken for granted. Earth’s gravity applies a force (weight)
that always pulls down, and it is what keeps objects and people on the
ground instead of floating around in midair. All forces are vector quantities
and therefore act in a single direction. The term net force refers to the total
force acting on an object.
Without a force being applied to them, objects would not move (or, if they
were already in motion, they would remain in motion without stopping).
Objects with a great deal of mass (such as a freight train) require a large
force to alter their motion. The goal of all mechanical technology is to most
effectively apply forces to the movement of varying mass quantities.
NEWTON’S LAWS OF MOTION
All mechanical devices take Newton’s laws for granted in their operation.
Newton’s first law describes the unchanging state of motion of an object
when it experiences no net force. A heavy crate suspended by a pulley is
only able to avoid crashing to the ground because the attached ropes fully
counteract the force of gravity pulling the mass downwards.
Newton’s second law can be summarized by the formula
F = ma
where m is measured in kilograms (kg), a is in meters per second squared
(m/s2) and F is in newtons (N). This law expresses the linear relationships
between either the mass of the moved object or the desired acceleration,
with the force required to achieve that movement.
One of the most important historical roles of machines has been in
multiplying the force a human or work animal provides in order to move
very massive objects that would be otherwise immobile. Ancient structures
including Stonehenge and the Egyptian pyramids are evidence of a long
human tradition of mechanical aids to labor.
Newton’s third law of motion states that for every action there is an equal
and opposite reaction. This law applies to all applications of force,
including those mediated by simple machines. It’s possible to pull on a
rope and pulley to li a weight only because the force of tension is carried
through a rope by a daisy chain of action-reaction force pairs from one
section of rope to the next.
Question
Analysis
Simple machines and other mechanical
Step 1: The question asks which statement
devices
applies to mechanical devices.
Step 2: Think about the traits that simple
machines and other mechanical devices have
in common: they are used to transfer force,
and they obey Newton’s laws.
Step 3: That’s as close as you can get to a
prediction with a general question like this, so
start evaluating answer choices.
Question
Analysis
(A) are technologies used to get around
Step 4: Mechanical devices use the laws of
certain laws of physics
physics; they don’t circumvent them, so (A) is
(B) are exclusively based on momentum
not correct.
(C) operate according to the rules of force and
Momentum is important, but it is not the only
mass
basis for any and all machines, so eliminate
(D) transmit and multiply force in order to
(B).
increase the amount of energy available
Choice (C) is true. Select it.
Choice (D) sounds almost correct, but how
does a device increase the energy available?
By burning fuel? By creating energy from
nothing? Simple machines like levers don’t
themselves burn up fuel. And although force
can be multiplied with mechanical advantage
(more on that later), energy cannot be created
out of nothing.
Now try one on your own.
According to Newton’s laws, an object being lifted by a
pulley will accelerate
(A) even if the applied force from the rope to the
object is a little less than the object’s weight,
because mechanical advantage makes up the
difference
(B) only if the net force on the object is zero and the
object is already in motion
(C) if the applied force from the rope to the object is
greater than the object’s weight
(D) if the object’s mass is greater than the applied
force
Explanation
Choice (C) is correct. There must be a non-zero net force for any object to
accelerate. Objects in motion where the net force is zero will continue
moving at a constant velocity, but will not accelerate. Both (C) and (D) talk
about a difference between two values, but answer choice (D) compares
the applied force to the object’s mass rather than weight. Since these
quantities have different physical meanings, it doesn’t make sense to say
one is greater than another.
Common Types of Forces
Learning Objectives
In this section you will learn to:
distinguish and understand the related terms of mass, weight,
and gravity, and apply a formula to calculate one value given the
others
understand friction as a responsive force and apply the formulas
for calculating kinetic and static friction
understand tension as a force found in a cable that stretches it
tight
understand hydraulic pressure as it relates to an applied force,
and as a transmitter or multiplier of force
apply the formula for torque as a measure of how effectively a
force can cause an object to rotate
GRAVITY AND WEIGHT
As seen previously, weight is different from mass. Mass is an intrinsic
property of matter, whereas weight is the force exerted on an object due to
gravity. The downward pull that the Earth exerts on bodies outside of itself
is a specific case of gravity at work. Weight can be easily measured using a
spring scale like that found in many people’s bathrooms, and the direction
of weight for all objects on Earth is the same: straight down toward the
center of the Earth.
The general formula for Newton’s Law of Universal Gravitation was given
in chapter 9: General Science. It can be used to explain why the same
person will weigh less on planets of different sizes and masses (for
example, when astronauts walked on the Moon, their weight was only of
what it was while on Earth). However, unless you are told otherwise, it is
safe to assume that for the purposes of everyday mechanical work the
location is here on Earth.
For bodies free-falling near the Earth’s surface, the acceleration due to
gravity (g) is calculated to be about 9.8 m/s2, ignoring air resistance. (Note
that “near the Earth’s surface” really means anywhere on Earth, including
on top of Mount Everest or parachuting from a plane thousands of meters
in the air. The value of g doesn’t change significantly at the top of a stair
ladder.)
Applying Newton’s second law, F = ma, for the specific case of weight, the
more general symbol for force, F, is replaced with the more specific force of
weight, W, and acceleration, a, is replaced with the constant value of
acceleration due to gravity, g. This results in the modified version of the
formula
W = mg
where W is weight in newtons (N), m is mass in kilograms (kg), and g is
acceleration due to gravity (either m/s2 or N/kg). To determine an object’s
weight in N, therefore, simply multiply its mass in kg by 9.8.
Study the example that follows, which does not have answer choices, to
help you practice predicting an answer to this type of question.
Question
Analysis
How many newtons of force due to gravity will
The question asks for the amount of force due
act on an 80 kg man while in a plane flying
to gravity.
over Denver, Colorado?
The man is not an astronaut (or if he is an
astronaut, he’s not currently in outer space or
on the Moon), so his weight will be pretty
much the same as any other 80 kg man on
Earth. This weight will be basically unchanged
whether he’s at sea level, in the United States’
highest-altitude large city, or in a plane flying
above that same city.
The phrase “newtons of force due to gravity”
is just another way of saying weight. Weight W
= (80 kg)(9.8 m/s2) = 784 N.
The answer is 784 N.
FRICTION
There are several responsive forces which act to resist movement. When
you move an object across a surface, the rubbing of the two surfaces
results in kinetic friction, which always acts in a direction opposite to the
motion of the object. Because it always opposes motion, kinetic friction
will eventually slow any moving object to a stop. Ice is polished to
minimize kinetic friction, but unless it is constantly being pushed, a hockey
puck will eventually slide to a stop in even the most slippery of rinks.
When an object is not moving, a force that attempts to slide it across a
surface will encounter a different type of friction. Attempting to push a
stationary box across a concrete floor will require a person to overcome
the static friction that opposes any attempted movement.
Both kinds of friction are based on two factors: the ) coefficient of friction,
µ (the Greek letter mu), which represents how much two materials resist
sliding against each other; and the ) normal force, FN, which represents
the equal and opposite force a surface exerts when an object presses
against it. The formulas for kinetic and static friction, respectively, are
Ff = µkFN
Ff = µsFN
where Ff stands for the force of friction and µk and µs stand for the
coefficients of kinetic and static friction. The coefficients of friction are
constant for any two surfaces in contact. The coefficients of friction are
dimensionless quantities, with no units of their own. Therefore, whatever
force unit is used to measure FN (N or lbs, for example), will also be used to
measure Ff.
Slippery surfaces like ice or wet asphalt have low coefficients of both
kinetic and static friction with most objects. Friction is directly
proportional to these coefficients. That’s why it’s important for drivers of
cars to understand that weather conditions can make braking to a stop
(which relies on the friction of the wheels with the road surface) less
effective.
Free Body Diagram of Forces Acting on a Sliding Object
For any given surface, the coefficient of static friction is higher than the
coefficient of kinetic friction. This means that more force is required to
initially get a stationary object moving than to keep it moving a erwards.
Once the large static friction force has been overcome and the object is in
motion, the smaller coefficient of kinetic friction takes over, and the
resistant force of friction decreases. This is why moving heavy objects
usually involves one extra big push at the beginning, but then a somewhat
smaller force for the rest of the trip.
One more important difference between static and kinetic friction is that
static friction only arises in response to an attempt to move an object along
a surface. Like the ) normal force that holds up objects with weight, it
responds to an applied force by matching and counteracting it. The
formula is actually used to determine the maximum of a variable value for
static friction, beyond which it breaks and an object will begin to move.
Both kinds of friction forces are directly proportional to the normal force of
the surface. As an experiment, try laying your palm flat and sliding your
hand along a nearby surface like a table or desk. Feel the resistance of the
movement due to kinetic friction. Now, with your palm still flat, try pushing
harder against the same surface, while still trying to slide your hand along
it.
Is it more difficult? If you push very hard against the surface, you may find
you are not even able to overcome the force of static friction and slide your
hand without decreasing the normal force first. When a person leans
against a wall, she allows a portion of the weight to push against the wall,
which pushes back with an equal and opposite normal force. This normal
force contributes to a corresponding static friction force that prevents the
person from sliding down the wall to the floor.
Most frequently, the normal force arises on flat horizontal surfaces as a
response to the weight of an object pressing it down. As a result, the
normal force is equal to an object’s weight much of the time, so that the
forces of friction are equal to the coefficients of friction multiplied by the
object’s weight. This assumption is false only on non-horizontal surfaces
(for example, slopes), or when additional forces are acting to push an
object down or hold it up.
Question
Analysis
Question
Analysis
A 15 kg object rests on a concrete floor, and
Step 1: The question asks for a prediction as
the coefficients of static and kinetic friction
to whether an object will move given an
are 0.3 and 0.2, respectively. If a continuous
applied force and taking into account friction.
force of 35 N is applied to the object in a
direction parallel with the floor, what will
happen?
Step 2: Comparing the applied force to the
frictional forces should make it obvious
whether the object will move or not. The
weight of the object will be equal to the
normal force holding the object up. Then the
force of friction can be determined.
FN = W = (15 kg)(9.8 m/s2) = 147 N
Ff = µkFN = (147 N)(0.2) = 29.4 N
Ff = µsFN = (147 N)(0.3) = 44.1 N
Step 3: The applied force of 35 N is less than
the maximum value for the force of static
friction. Since the object is already at rest, and
the applied force is not enough to “break” the
force of static friction, the net force will be
zero and the object will stay put. The lesser
force of kinetic friction is irrelevant since the
object will not slide to begin with.
Question
Analysis
(A) The object will be bounced back due to
Step 4: Answer choice (B) is correct. (The key
friction.
is that an object at rest must experience a
(B) The object will remain at rest as the
large enough applied force to overcome static
applied force is unable to overcome the static
friction before kinetic friction becomes
friction.
relevant.)
(C) The object will initially move but then stop
as kinetic friction overcomes the applied
force.
(D) The object will accelerate continuously.
Now you try one:
Four objects of the same material and dimensions, but
different weights, are placed on four different
tabletops. When a force is applied that causes the
boxes to move, which one generates the greatest
amount of kinetic friction?
(A)
(B)
(C)
(D)
Explanation
Answer choice (C) is correct. According to the formula for kinetic friction,
the box with the greater weight will have the greater normal force and thus
greater frictional force compared to one of less weight. The oily surface will
have a lower coefficient of friction than the dry surface. Therefore, the
heaviest box on the driest surface will experience the most friction.
Another responsive force comes from air resistance, sometimes known as
air friction but more commonly known as drag. Drag opposes movement
not across a solid surface but through a fluid, like water or air. The two
main variables that affect drag are cross-sectional area and speed. Highperformance cars, boats, and aircra are designed to be sleek and pointy,
to minimize the area of the side that is plowing through the air or water.
Parachutes work by intentionally increasing area for a skydiver, so that
drag is increased and the person can be slowed down to a safe speed
before hitting the ground.
TENSION
When cables are used to pull an object, an applied force exerted on one
end results in the attached object receiving the same pulling force from the
other end. When force is transmitted through rope or other pullable
materials, the internal stretch force of the material is called tension.
Tension can be measured in N or lbs, or any other force unit measurement.
As a simplification, tension is o en assumed to be equal in all parts of the
material. This assumes, however, that the mass of the material under
tension is either zero or negligible. In reality, tension is greatest where the
force is being applied. To understand why this is, imagine a 100-pound
weight suspended from a 10-pound chain. The bottommost link in the
chain has an important job: it’s holding up the 100-pound weight. The
tension at this point in the chain, therefore, is 100 pounds.
But the chain link just above it also has an important job. It’s holding up
the link that’s holding up the 100-pound weight, which means it must have
a tension equal to 100 pounds, plus the weight of one chain link. If you
continue to the top of the chain, where the applied force is holding it in
place, the topmost link is responsible for not only the 100-pound weight,
but for another 10 pounds from the chain itself. At this section of the chain,
the tension is 110 pounds.
The takeaway from this is that, barring imperfections or weaknesses in the
material under tension, the most likely place for a rope or cable to snap is
not near the object it is holding or pulling, but near the place where the
rope or cable is itself being pulled. When a winch (a mechanical device
used to wind a rope) draws in a heavy-duty cable and the tension exceeds
the material’s tensile strength, it will likely snap very close to the winch,
rather than close to the load.
Question
Analysis
A concrete block is suspended by two steel
Step 1: The question asks for the tension of
cables, spaced equidistant from the edges.
one of two cables from which a weight is
What best describes the value of T1?
suspended.
Question
Analysis
Step 2: The system is in static equilibrium.
Since the block is remaining in one place
without accelerating, the net force is zero and
the downward force due to gravity must be
exactly balanced by the tension in the two
cables. Each cable must contribute half of the
upward force (tension).
T1 + T2 = 50 N
T1 = T2 = 25 N
Step 3: The tension in the first cable must be
equal to half of the downward force on the
block.
(A) 5 N
Step 4: Choice (B) is correct.
(B) 25 N
(C) 50 N
(D) 100 N
Now try one on your own.
Using a cable attached at one end, a force is applied to
a slab of metal. At which point along the cable is the
cable most likely to snap?
(A) A
(B) B
(C) C
(D) It is equally likely to break at any point along the
rope.
Explanation
Choice (C) is correct. The force applied to the cable will result in
acceleration of the metal slab. However, the metal slab by itself requires
less force than the slab and cable combination. Thus, more force is applied
at the end of the cable where the force is applied compared to what is
actually acting on the metal slab itself. This corresponds to a greater
tension near point C compared to points B and A. If the cable were to snap,
it would likely happen where there is higher tension.
HYDRAULIC PRESSURE
Fluid power can also be used to gain mechanical advantage. Hydraulics is
the transmission of force through the use of liquids. While the classic
simple machines are effective and reliable for many purposes, hydraulics is
a little more versatile at redirecting and multiplying forces in complex
systems. In order to understand how hydraulics works, it is first necessary
to have a grasp of the concept of pressure. If force is applied evenly over a
certain area, then pressure is applied to that area. Pressure is calculated
using the formula
P=
where F is force in pounds (lb), A is area in square inches (in2), and P is
pressure in pounds per square inch (psi). While other applications of
pressure in physics and chemistry use standard units of newtons and
square meters, the above units are more common in hydraulics. Keep in
mind that F is divided by A. A force of 100 pounds applied over an area of 10
square inches results in a pressure of 10 psi being developed.
Using the formula for pressure, you can derive F = PA, which is useful for
calculating the amount of force that is developed when pressure P is
applied to area A.
Even when extremely high pressure is applied to a liquid, the volume of the
liquid will decrease only a very small amount. This property of nearincompressibility makes liquids very effective at transmitting force, as no
force (or very little) is used up in compressing the liquids into a smaller
space. Liquids also tend to take the shape of their container, filling up any
available space (given enough of the liquid). According to Pascal’s law
(discovered by French mathematician and physicist Blaise Pascal in the
seventeenth century), the pressure in any part of an enclosed fluid is the
same and points in all directions.
Putting it all together, applying force to one end of a hydraulic system will
increase the pressure everywhere, which, when applied to an area of the
same size, produces the same force at a different location and in a different
direction. Changing the area over which force acts can also change the
magnitude of the force. In a hydraulic system, a smaller force is applied
over a greater distance to produce a greater force over a smaller distance.
Hydraulic Li
Try your hand at a problem about pressure.
Pressure is equal to force acting over
(A)
(B)
(C)
(D)
a distance
a period of time
a volume
an area
Explanation
Choice (D) is correct. Pressure is equal to force acting over an area.
TORQUE
) Torque measures how much a force is able to cause an object to rotate.
Torque, like pressure, cannot be properly called a force itself. The formula
for torque is
τ = rF
where torque (τ, the Greek letter tau) is the product of an applied force (F)
perpendicular to the lever arm of the rotated object, and the length of the
lever arm (r), measured from the pivot point (center of rotation) or fulcrum,
to the point where the force is being is applied. Force is normally measured
in either N or lb and the length of the lever arm in m or . Torque may
therefore be measured in standard N-m (newton-meters) or the -lb (footpound) unit.
However, remember this length measurement is perpendicular to the force
applied in rotating the object, not parallel, so torque is not equivalent to
work, whose N-m units (more o en expressed as joules, J) represent a
force applied through a distance. (Nor is torque equivalent to energy, also
measured in J.)
Torque Applied via a Wrench
Torque is directly proportional to the force applied to rotation, and is also
proportional to the distance from the center of rotation where the force
acts. Applying a force at the farthest end of a lever arm is advisable in
getting the greatest possible torque. When a mechanic applies his
maximum force but is unable to turn a difficult bolt, a longer wrench may
do the trick. This doesn’t increase the force he is able to apply, but the use
of a longer lever arm for the same force does result in increased torque and
therefore, hopefully, better success in loosening the bolt. Unlike work, an
object does not have to be successfully rotated before a torque is said to
have been applied.
Question
Analysis
How much force is needed to apply 50 -lb of
Step 1: The question asks for the amount of
torque to a bolt using a 2 long wrench?
force applied to a lever arm for a certain
torque.
Step 2: The torque formula relates length,
force, and torque. To solve this question,
isolate force and plug in values.
Based on the units in this question, force is
measured in pounds (since pounds multiplied
by feet is the only way to get foot-pound units
for torque).
τ = rF
F = τ/r = (50 -lb)/(2 ) = 25 lbs
Step 3: The force must be 25 lbs, not 25 N.
(A) 100 lbs
Step 4: There is only one perfect match:
(B) 50 N
choice (C).
(C) 25 lbs
(D) 25 N
Now try a question about torque on your own.
Which of the following applied forces will result in the
greatest torque?
(A)
(B)
(C)
(D)
Explanation
Choice (A) is correct. The product of the force and the length of the lever
arm, where the two quantities are perpendicular to each other, produces
torque. For (A), τ = (1.5 m)(50 N)=75 N-m, compared to 60 N-m in (B) and 70
N-m in (C). (D) provides no torque at all. Although there is a large applied
force, it is pushing along the lever arm toward the fulcrum, and cannot
result in any rotation.
Energy, Work, and Power
Learning Objectives
In this section you will learn to:
compute values for kinetic and potential energy
apply the principle of conservation of mechanical energy
calculate the amount of work performed on an object
ENERGY
In a broad sense, energy is the capacity to cause a change in the state of
something. Energy can take many different forms, but the Mechanical
Comprehension portion of the ASVAB deals largely with the type called
mechanical energy. In order to answer questions on the MC test, you will
need to understand the two different types of mechanical energy: kinetic
and potential.
Kinetic energy is the energy of movement. Your personal observation
likely tells you that a baseball thrown by a major league pitcher at 40
meters per second has more kinetic energy than a pitch that you might
throw at 25 meters per second. Similarly, a car traveling at 10 meters per
second has more kinetic energy than a bicycle traveling at the same speed.
So you could say that kinetic energy must be a function of both mass and
velocity, and you would be correct.
The formula to calculate kinetic energy (KE) is:
KE =
mv2
where m is mass in kilograms (kg), v is speed in meters per second
,
and KE is kinetic energy in a standard unit called joules (J), which has the
units
. Note that KE is a linear function of mass but the velocity
component is squared. Here is how the formula could be applied:
Question
Analysis
Truck A has a mass of 10,000 kg and is
Step 1: The question asks for the ratio of the
traveling at a speed of 30 m/s. Truck B has a
KEs of the two trucks, not the actual values.
mass of 5,000 kg and a speed of 15 m/s. What
is the ratio of the kinetic energy of Truck A to
that of Truck B?
Step 2: The values needed to calculate KE for
both trucks are given, so no further
simplification is necessary.
Step 3: Use relationships rather than actually
calculating. Both the mass and speed of A are
2 times those of B. The masses by themselves
cause the KE of A to be greater by a factor of 2.
Since KE is a function of v2, the KE of A is 22
times that of B due to speed. In total, A’s KE is
4 × 2 = 8 times that of Truck B.
Question
Analysis
(A) 1:8
Step 4: Select choice (D). Double check that
(B) 2:1
the question asked for the KE ratio of A:B and
(C) 4:1
that calculations are correct.
(D) 8:1
Try this problem on your own. This question does not have answer choices.
If an automobile with a mass of 1,500 kg is traveling at
72 kilometers per hour, what is its kinetic energy in
joules?
Explanation
Note that the units of joules
are not the same as the units in
the problem. To convert, first restate the speed as 72,000 meters per hour.
Since there are 60 seconds in a minute and 60 minutes in an hour, there are
3,600 seconds in an hour. Now you can set up the calculations:
Potential energy (PE), as the name implies, is energy that has the
potential to be converted to kinetic energy. Many ASVAB questions use one
particular type of PE, gravitational potential energy. If you hold an object
in your hand raised above the floor and then let it fall, its potential energy
is fully converted to KE by the time it hits the floor. The higher the object is
raised, (h), the greater the potential energy of the object. Since heavy
objects and light objects fall at the same rate, a heavier object released
from the same height would have greater KE when it hits the floor and
therefore greater PE when held above the floor. The force acting on the
dropped object is, of course, gravity. If you were to drop an object from the
same height on the Moon, the speed when it hit the ground would be less
than on Earth because the pull of gravity is much lower. Therefore, the
object’s PE would be less on the Moon.
The formula to calculate gravitational potential energy follows the logic
above.
PE = mgh
where m is mass in kilograms (kg), g is acceleration due to gravity
, h is the height of the object in meters (m), and PE is gravitational
potential energy measured in joules (J).
On the ASVAB, it does not matter whether the object is dropped or rolled
down a rampInclined planes#gravitational potential energy because minor
factors such as friction will be ignored on energy problems; the velocity,
KE, and PE will be the same in either case, even though it will take longer
for the object on the ramp to reach the ground.
Study the following example problem, which does not have answer
choices, to help you practice making a prediction on a question of this
type.
Question
Analysis
What is the potential energy of a 0.5 kg ball
The question asks you to calculate potential
held at the top of a building 20 meters above
energy.
the ground?
The question provides two of the variables
you need to calculate PE, mass (m) and height
(h).
It would be a good idea to memorize that g =
9.8 m/s2 or at least that it is approximately 10.
PE = mgh = 0.5 × 9.8 × 20 = 98 joules (J)
The answer is 98 J.
A falling object has its potential energy (PE) converted into kinetic energy
(KE) as it falls. Since the ASVAB ignores such minor factors as resistance on
energy problems, problems in the MC section will adhere to the principle
of conservation of mechanical energy. This rule states that the total
mechanical energy (PE + KE) remains constant as long as no other forces
are applied. A er the object is dropped but before it hits the ground, it will
have some KE and some PE, totaling up to the initial PE. At the instant it
hits the ground, all of the initial PE will have been converted to KE. See how
this principle is used to solve the following problem:
Question
Analysis
A 1.63 kg object is dropped from a height of
Step 1: You are asked to calculate the velocity
2.5 meters. What will its velocity be at the
when the object hits the ground.
moment it hits the ground?
Question
Analysis
Step 2: You are given the mass and height of
the object but nothing about velocity. There is
nothing to simplify.
Step 3: The initial PE equals the final KE, so
mgh =
. Notice that m appears on
both sides of the equation so it cancels out:
Multiply both sides by 2 for ease of calculation
to get
9.8 × 5 = 49 = v2
v=7
(A) 7 m/s
Step 4: Select choice (A). By setting PE = KE
(B) 14 m/s
you followed the principle of conservation of
(C) 28 m/s
mechanical energy and the variable v is the
(D) 49 m/s
answer to the right question.
If an object is thrown straight up into the air rather than being dropped,
when the object reaches its highest point just before it begins to descend,
its KE = 0 and the potential energy it has at this point equals the kinetic
energy it had when it was first thrown. Apply this concept to the problem
below:
Question
Analysis
Question
Analysis
Joel throws a ball straight up in the air at a
Step 1: You are given an initial velocity, the
velocity of 30 m/s. When he releases the ball,
additional fact that the ball is released 2
it is 2 meters above the ground. What is the
meters above the ground, and the knowledge
ball’s approximate maximum height above
that the answer will be an approximation.
the ground?
Step 2: The question asks for the maximum
height above the ground rather than above
the point of release.
Step 3: Set PE = KE: mgh =
. Cancel
out m and plug in v, and g = 10 since the
question asks for an approximate value.
Add 2 meters to get the total height, 47. Since
you used 10 for g rather than 9.8, the true
value will be greater than 47.
(A) 40 meters
Step 4: Only (C) and (D) are greater than 47,
(B) 45 meters
but (D) is clearly too high. (C) is correct. Check
(C) 48 meters
the math and that the question requires the
(D) 60 meters
additional 2 meters.
WORK
Work is accomplished when force is applied to move an object. Like the
formulas for energy, the formula to calculate work coincides with what you
can observe in the real world. The more force that has to be exerted to
move an object a certain distance, the more work is done. Similarly, the
farther an object is moved by exerting force, the more the work. These
facts are summarized by the formula:
W = Fd
where W is work in joules (J), F is force in newtons (N), and d is distance in
meters (m).
If a force of 100 N is applied to a car, and the car is moved 10 meters, then a
total of 100 × 10 = 1,000 joules of work has been done.
Force F Pushing a Car over Distance d
If force is applied to the car, but the car does not move, no work has been
done. This can be seen in the formula W = Fd, where zero distance (d)
results in work (W) being zero as well. No matter how much force is
applied, no movement results in zero work being accomplished.
Note that work and kinetic energy are both measured in joules. This is not
a coincidence, as any work that is done to accelerate an object at rest to
velocity v will be converted into the kinetic energy of that object. This
principle is known as the work-energy theorem.
Question
Analysis
A force of 10 N is applied to a stationary object
The question has values for F, m, and v and
with 1 kg mass for a sufficient time to attain a
asks how much work was done to attain that
velocity of 4 m/s. How much work was done
velocity.
to accomplish this?
Work can’t be calculated directly because the
distance isn’t known. However, W = KE, per
the work-energy theorem.
Plug the known values into the equation and
solve.
Answer: 8 joules
Apply the information in this section to answer the problem below.
Jane pushes a 20 kg box 20 m in 20 seconds by
pushing with a constant force of 10 N. Kellen pushes a
40 kg box 10 m in 15 seconds by pushing with a
constant force of 20 N. Which person did more work?
(A) Jane
(B) Kellen
(C) They both did the same amount of work.
(D) It cannot be determined from the information
given.
Explanation
The data regarding the mass of the boxes and the time it took each person
to move a box are irrelevant. Jane accomplished 10N × 10 m = 200 J of
work; Kellen’s work was 20N × 10 m = 200 J. Therefore, (C) is correct.
POWER
Power is the rate at which work is done:
Consider the example of a woman pushing a small car over a distance of
100 meters. If the woman pushes with a force of 100 N to move the car,
then using W = F × d, you can see that 100 N × 100 m = 10,000 J of work has
been done. If she accomplishes the task at a constant rate over the course
of 500 seconds, then the power applied was
. If another
woman can do the same amount of work in 250 seconds, then that woman
has twice as much power, or
.
One common unit used to express power is the watt, which equals
or
The watt is named a er James Watt, an engineer who died in 1819
and whose work on the steam engine helped make the Industrial
Revolution possible. The unit of power that many people in the United
States are more familiar with is horsepower, since this is the unit that is
used to rate internal combustion engines. Horsepower uses a different
system of measurement: it is defined as 550 foot-pounds per second of
work being done. One horsepower is the equivalent of 746 watts. Study the
example below, which is presented without answer choices, in order to
help you practice predicting on a question of this type.
Question
Analysis
Jane pushes a 20 kg box 20 m in 20 seconds
You are asked to calculate how much power
by pushing with a constant force of 10 N. How
Jane exerted.
much power did she exert?
You already know that Jane did 200 J of work.
Since she accomplished that in 20 seconds,
the power she applied was 10 watts.
Simple Machines
Learning Objectives
In this section, you will learn how to:
identify simple machines and their uses
calculate the mechanical advantage of specific simple machines
determine forces in simple machine problems
Simple machines were invented centuries ago to reduce the force or effort
needed to perform a variety of tasks; heavy objects need to be li ed, parts
need to be pushed together or pulled apart, and large machines need to be
moved. O en, it is difficult or impossible for a human being to apply
enough force to get the job done.
In order to increase the available force to a much larger one, mechanical
advantage is used. Mechanical advantage is defined as “the advantage
gained by the use of a mechanism in transmitting force.” Using the proper
equipment, it is possible to increase the force applied severalfold.
However, while mechanical advantage can be used to amplify force, this is
accomplished by exerting a force over a greater distance. In other words,
the work output can never exceed the work input. The good news,
however, is that simple machines can make hard work easier by breaking it
down into smaller, more manageable pieces.
The efficiency of a machine describes how much of the power inputted
into the machine is turned into movement or force. A machine that turned
100 percent of the power applied to it into outputted force would have 100
percent efficiency. In the real world, however, no machine is 100 percent
efficient, because all machines are affected by friction and most are
affected by worn-down and/or imperfectly fitted parts.
INCLINED PLANE
One of the simplest ways of managing li ing tasks is through the use of the
inclined plane. Li ing a 100 kg (about 220 pound) box is a difficult, if not
impossible, task for one person. However, the use of an inclined plane (or
ramp) can make this a manageable chore.
Pushing a Box Up a Ramp or Li ing It to Height h
Remember that the work that is done to li the box will be the same as the
final gravitational potential energy of the box (PE = mgh). Therefore, the
same amount of work will be done whether the box is pushed up the ramp
(assuming no friction), or if it is li ed directly. The difference with the ramp
is that a much smaller force can be applied to raise the box. This force must
be applied over a longer distance, but it will give some mechanical
advantage to make the task easier. Study the following problem to see how
much the mechanical advantage of inclined planes can reduce the force
needed to raise a heavy object.
Question
Analysis
Jose has to push an object that weighs 1,000
The question asks you to calculate force and
N up an inclined ramp to a height 2 m above
ignore friction.
its current location. If the ramp is 20 m long
(measured up the slope), how much force will
Jose have to use if the effects of friction are
ignored?
When Jose has completed the task, the object
will have 2 m × 1,000 N = 2,000 J greater
potential energy than when he started, so he
will have to accomplish 2,000 J of work. Since
W = f × d and the ramp is 20 m in length, he
will only have to exert
= 100 N.
The answer is 100 N.
WEDGE
The wedge is a variation of the inclined plane. While the inclined plane
stays stationary, the wedge is designed to move. It can be used for many
purposes, including li ing, splitting, and tightening. The mechanical
advantage that can be gained with a wedge is determined by the ratio of its
length to its height.
Wedge
Making the wedge longer relative to its height (that is, with a smaller slope)
will decrease the amount of li that takes place as the wedge is moved
horizontally. This increases the amount of force that can be generated by
the wedge and makes it easier to li heavy objects. Remember that if force
is increased by the wedge, then the distance it will li will be less than the
distance it moved horizontally.
Common applications of the wedge include knives, chisels, and log
splitters.
LEVERS
Another simple machine that can be used to amplify force or distance, as
well as change direction, is the lever. There are three basic types of levers,
so this machine lends itself to many different applications.
The first-class lever is used to increase force or distance, and to change
the direction of the force. An example of a first-class lever is a child’s teetertotter.
First-Class Lever
The fulcrum is the point upon which the lever pivots. When force is applied
to one end of the lever, the movement at the other end is in the opposite
direction. The position of the fulcrum will define whether any mechanical
advantage is gained. If the fulcrum is closer to the object being li ed, less
force is required to do the work. However, the end that the effort is applied
to must move farther to get the job done.
The opposite effect takes place when the fulcrum is moved closer to where
the effort is applied. Now the distance the object can be moved is
amplified, but the force required is increased.
The mechanical advantage gained by the use of a lever is simply the ratio
of the distance of the applied force from the fulcrum to the distance of the
object from the fulcrum. Thus, a lever where the force is applied 3 meters
from the fulcrum and the object being acted upon is 1 meter from the
fulcrum will have a mechanical advantage of 3:1. The force applied will
move 3 times as far as the object but the force on the object will be 3 times
as great as the force applied.
A second-class lever is used to increase force on the object in the same
direction as the force applied. This type of lever requires a smaller force to
li a larger load, but the force must be exerted over a greater distance. An
example of a second-class lever is a wheelbarrow.
Second-Class Lever
The mechanical advantage of the second-class lever increases as the
object is moved closer to the fulcrum. This can also be accomplished by
increasing the length of the lever. The following example illustrates the
mechanical advantage of a second class lever:
Question
Analysis
Which of the following forces would be the
Step 1: The question asks for the minimum
least needed to li a 10 N object placed 0.5 m
force needed to li the object given the
from the fulcrum of a second-class lever if the
dimensions of the lever.
li ing force is exerted 2 m from the fulcrum?
Step 2: The problem provides the weight of
an object and the measurements of a secondclass lever that is used to li the object.
Step 3: The mechanical advantage of the
lever is
= 4, so a force of
the weight of
the object or 2.5 N is needed. However, this
amount of force would balance the downward
and upward forces, so the correct answer
must be > 2.5 N.
Question
Analysis
(A) 0.5 N
Step 4: Choose option (C). Verify that this is
(B) 2 N
the minimum force needed from among these
(C) 3 N
choices (that’s why (D) is incorrect), and
(D) 10 N
double check the dimensions and
calculations.
The third-class lever is also used to increase distance traveled by the
object in the same direction as the force applied. It is similar to the secondclass lever in that the fulcrum is at one end. The object, however, is at the
other end of the lever, with the force being applied somewhere in between
the fulcrum and the object. Examples of third-class levers would be a
fishing pole and a catapult.
Third-Class Lever
Since the distance moved at the point where the force is applied is less
than the distance traveled by the load with a third-class lever, the force
needed is increased. This effect magnifies as the force is applied closer to
the fulcrum.
PULLEYS
Applying force to an object is sometimes accomplished through the use of
a pulley. A pulley is a system that is used to change the direction, but not
the amount, of a force.
Person Pulling a Rope Through a Pulley to Li an Object
A pulley system consists of a rope, belt, or chain looped over a wheel. It can
be useful in certain situations because it is o en easier to pull with a
downward force than an upward force.
BLOCK AND TACKLE
It is relatively uncommon for one pulley to be used by itself. O en, two or
more pulleys will be used in an arrangement known as a block and tackle
to increase li ing force.
Block and Tackle
The block and tackle shown here has four pulleys; two are attached to a
stationary object (such as the ceiling or wall of a building) and the other
two are attached to the lower block (the load). As the rope is pulled, the
lower block moves toward the stationary pulleys. Note that in order to li
the load 1 foot, it is necessary to pull the rope a total of 4 feet. This is
because each of the four rope links must shorten by 1 foot to get the lower
block to move 1 foot. Neglecting friction, this gives a total mechanical
advantage of 4:1, so if 4 pounds of force are required to li a load, only 1
pound needs to be applied to the rope. Note that you can determine the
mechanical advantage ratio of a block and tackle system by counting the
number of pulleys.
WHEEL AND AXLE
The wheel and axle mechanism is not just a simple free-turning wheel
such as the front wheel of a typical bicycle. Instead, this type of machine
uses two wheels mounted on a sha , with one wheel having a larger
diameter than the other. The wheel and axle can be used to increase
mechanical advantage. An example of a wheel and axle is the steering
wheel of a car.
Wheel and Axle
The large-diameter wheel will usually be the one that has the effort applied
to it. Large movements of the large wheel result in small movements of the
small wheel. The larger wheel has a greater circumference, so a point on
the edge of it travels further per turn compared to a point on the smaller
wheel. Since a large movement (or distance) is being translated into a
small movement, the force is then being increased. The amount of
mechanical advantage is determined by the ratio of the diameters of the
wheels. If the large wheel is 20 inches in diameter, and the small wheel is
10 inches in diameter, the total mechanical advantage is 2:1.
GEARS AND GEAR RATIOS
Gears can be used anywhere that force is being transmitted between two
points, and are excellent for gaining mechanical advantage.
Meshed Gears
Gears can be used to change rotational speed and torque. The gear ratio is
determined by comparing the number of teeth on the large gear to the
number on the small gear. In the figure, the large gear has 18 teeth and the
small gear has 12, so the gear ratio is 3:2.
If a small gear drives a large gear, a speed reduction takes place. The large
gear will turn more slowly than the small gear and the speed of the output
will be slower in proportion to the gear ratio. However, an associated
torque multiplication (increase) will take place, and the torque output of
the large gear will be greater than what was applied to the small gear, in
proportion to the gear ratio. A speed decrease means that torque will
increase. A mathematician would describe these two properties as
inversely proportional.
Check your understanding of gears with this problem:
Question
Analysis
Gear A in the figure above turns counter-
Step 1: The question asks both the direction
clockwise at the rate of 60 revolutions per
and the rotational speed of Gear B.
minute (RPM). In what direction and at what
rate will Gear B turn?
Question
Analysis
Step 2: The relationship of the gears, the
number of teeth on each, and the RPM and
direction of Gear A are given. No
simplification is needed.
Step 3: The two gears move in opposite
directions, so eliminate answer choices (C)
and (D). Since Gear B is larger and has more
teeth, it must turn more slowly.
(A) clockwise at 40 RPM
Step 4: The correct answer is (A). The gear
(B) clockwise at 90 RPM
ratio is 3:2 and the ratio of the rate of
(C) counter-clockwise at 40 RPM
revolutions is 2:3, so the answer checks
(D) counter-clockwise at 90 RPM
correctly.
Mechanical Comprehension Practice Set
1
Select the best answer for each question. This question set has 15 practice
questions, which is the number of Mechanical Comprehension questions
you will see if you take the CAT-ASVAB.
1. The work required to li an object is the same as
(A)
(B)
(C)
(D)
the change in potential energy of the object
the weight of the object divided by gravity
the force required to overcome friction
half of the work required to put the object down
2. A constant force of 2 N is applied to a mass of 6 kg that is initially at rest
for 3 seconds. Assuming there is no friction or any other force applied to
the mass, what is the velocity of the mass a er 3 seconds?
(A) 0.5 m/s
(B) 1.0 m/s
(C) 6.0 m/s
(D) 12.0 m/s
3. Approximately how much force is needed to li the weight below?
(A) 6 lbs
(B) 12 lbs
(C) 24 lbs
(D) 48 lbs
4. If a ball is dropped from a height of 5 m, what will be its approximate
speed when it hits the ground?
(A) cannot be determined because the mass is unknown.
(B) cannot be determined because the time it takes to reach the ground
is unknown.
(C) 5 m/s
(D) 10 m/s
5. Adam’s car is stuck in the mud, so he recruits some friends to help push it
out. If they apply 2,000 N of force to push the car 5 m, how much work did
they accomplish?
(A) 400 J
(B) 1,000 J
(C) 2,000 J
(D) 10,000 J
6. A machine in an assembly plant li s parts weighing 10 N each from the
floor to a height of 2 m. If this machine must li batches of 20 parts at a
time in 2 seconds, what amount of power is required?
(A) 20 watts
(B) 100 watts
(C) 200 watts
(D) 400 watts
7. A man who weighs 900 N wants to compress some loose soil in his
garden, so he puts a thick plate that is
m wide and
m long on the ground and stands on the plate. Assuming that the plate
distributes his weight evenly, how much pressure is applied to the soil?
(A) 900
(B) 1600
(C) 1800
(D) 2400
8. Gear A has 15 teeth and gear B has 10. If gear A makes 14 revolutions, how
many will gear B make?
(A) 7
(B) 14
(C) 21
(D) 28
9. Two wheels are secured to a common axle. If the larger wheel has a
radius of
m and the smaller wheel has a diameter of
m, what is the mechanical advantage for a force applied to the larger
wheel?
(A) 5 to 1
(B) 10 to 1
(C) 20 to 1
(D) 40 to 1
10. A basic kitchen knife, like the one below, is based on which of the
following simple machines?
(A) wedge
(B) first-class lever
(C) pulley
(D) second-class lever
11. How much force is needed to apply 50 -lb of torque to a bolt using a 2
long wrench?
(A) 100 pounds
(B) 50 pounds
(C) 40 pounds
(D) 25 pounds
12. If a 10 N force applied to an object produces an acceleration of 10 m/s2,
assuming friction is NOT negligible, what could the mass of the object
have been?
(A) less than 1 kg
(B) equal to 1 kg
(C) between 10 kg and 1 kg
(D) greater than 10 kg
13. The force of friction between two surfaces moving past each other DOES
NOT depend on
(A) the normal force
(B) the nature of the surfaces in contact with each other
(C) the area of the surfaces in contact with each other
(D) the speed at which the surfaces are moving past each other
14. The gravitational acceleration on Earth, g, is 9.8 m/s2. The gravitational
acceleration on a neighboring planet, Xendor, is 3 times as much. What is
the approximate weight of a 100 kg person on Xendor? (Hint: you can
approximate the gravitational acceleration on Earth as 10 m/s2 to make
calculations easier.)
(A) 100 N
(B) 300 N
(C) 1,000 N
(D) 3,000 N
15. Assuming no friction, if 80 J of work was done to move an object 2 m,
what was the net force that was applied?
(A) 4 N
(B) 16 N
(C) 40 N
(D) 160 N
Mechanical Comprehension Practice Set
2
Select the best answer for each question. This question set has 15 practice
questions, which is the number of Mechanical Comprehension questions
you will see if you take the CAT-ASVAB.
16. A man pushes against an object at rest, but fails to get it moving. Which of
the following must be true about the relationship between the applied
force and the force of friction?
(A) The applied force is less than the force of static friction.
(B) The applied force is equal to the force of kinetic friction.
(C) The applied force is equal to the force of static friction.
(D) The applied force is greater than the force of static friction.
17. A ball with a mass of 10 kg starts rolling down a hill 20 m high. What is its
approximate velocity when it hits the bottom, ignoring resistance?
(A) 10 m/s
(B) 15 m/s
(C) 20 m/s
(D) 40 m/s
18. A 500 g block made from a uniform material is suspended from the ceiling
by two equal length ropes equidistant from the center of the block, as
depicted in the figure below. Which of the following best approximates
the tension in rope 1 (T1)?
(A)
(B)
(C)
(D)
2.5 N
5.0 N
50 N
250 N
19. A hydraulic li is set up as depicted below. Which of the following must be
true?
(A) The work done by Force 2 is greater than the work done by Force 1,
since Force 2 is applied over a longer distance.
(B) To do the same amount of work, Force 2 must be smaller than Force
1, but applied over a larger distance.
(C) Force 1 must be greater than Force 2, because more work must be
done by Force 1.
(D) The pressure in the le side of the li must be greater than the
pressure in the right side of the li , since Force 1 is larger.
20. Two weights, one with a mass of 10 kg and another with a mass of 20 kg,
are placed on opposite ends of a 9 m rod. To achieve rotational
equilibrium, what distance from the 10 kg weight must the fulcrum be
placed?
(A)
(B)
(C)
(D)
3.0 m
4.5 m
6.0 m
8.0 m
21. What is the kinetic energy of a 98 N object moving at 100 m/s?
(A) 10,000 J
(B) 50,000 J
(C) 100,000 J
(D) 500,000 J
22. A man pushes a 50 kg block a distance of 10 meters in 20 seconds with a
force of 100 N. How much power did he exert?
(A) 25 W
(B) 50 W
(C) 100 W
(D) 200 W
23. Based on the diagram below, approximately what minimum force must
be applied to the rope to li the object?
(A)
(B)
(C)
(D)
25 N
50 N
100 N
250 N
24. Snowshoes are used to reduce the pressure exerted by the feet when
walking on top of deep snow. A 150 lb woman puts on two rectangular
snowshoes with dimensions 10 inches by 15 inches each. What pressure
does the woman exert on the snow while both shoes are equally bearing
her full weight?
(A) 0.5 psi
(B) 1.0 psi
(C) 5.0 psi
(D) 10.0 psi
25. A 40 kg block is sitting on a table and it is also pushed down by a 100 N
force. What is the magnitude of the normal force provided by the table if
the object remains at rest? (Use 10 m/s2 for gravity.)
(A) 140 N
(B) 300 N
(C) 400 N
(D) 500 N
26. A ball with a mass of 5 kg is thrown from a height of 10 meters at an angle
of 30° above the horizontal with an initial velocity of 10 m/s. Consider any
resistance to be negligible. What is the approximate total kinetic energy
when the ball hits the ground?
(A)
(B)
(C)
(D)
250 J
300 J
500 J
750 J
27. Which of the answer choices best describes the topics that are included in
the area of physics known as “mechanics?”
(A)
(B)
(C)
(D)
the proper use of tools and measuring devices
machines that transmit or use energy
the laws of motion, energy, and forces
the laws of trajectories, energy, and forces
28. Once sufficient force is applied to a stationary object to overcome static
friction, if the same force is maintained, the object will accelerate. This is
true because __________.
(A) the force that is applied accumulates
(B) the coefficient of kinetic friction is greater than the coefficient of
static friction
(C) the coefficient of static friction is greater than the coefficient of
kinetic friction
(D) the object's momentum is cumulative
29. Playground seesaws are constructed in the same way as first-class levers.
A boy wants to play on the seesaw with his little brother. The big brother
weighs 100 pounds; the little brother weighs 75 pounds and sits 8 feet
from the center of the seesaw. In order for the two brothers to be
balanced, how far from the center of the seesaw should the big brother
sit?
(A)
(B)
(C)
(D)
6.0 feet
8.0 feet
10.0 feet
12.5 feet
30. A hydraulic li has a 2 cm diameter piston that exerts a downward force
of 20 N on the incompressible fluid in a closed system. If the piston that is
at the other end has a diameter of 20 cm, how much upward force can it
exert?
(A)
(B)
(C)
(D)
20 N
200 N
1,000 N
2,000 N
Answers and Explanations
MECHANICAL COMPREHENSION PRACTICE SET 1
1. A
The work-energy theorem states that work performed on an object will
increase the object’s mechanical energy by the amount of work applied
to the object. In this case the increase in mechanical energy was the
additional potential energy resulting from the object being li ed higher.
Therefore the final PE equals the work.
2. B
Since F = ma, then a =
acceleration × time. Therefore:
. Change in velocity =
.
3. B
This block and tackle has 2 pulleys, so the mechanical advantage is 2:1,
because the weight will only move half the distance that the rope is
pulled. As a result, the force applied will be half the weight, or 12 lbs.
4. D
Although the mass and time are unknown, they are not needed to solve
the problem. When the ball is 5 m above the ground all its energy is PE,
but when it hits the ground all its energy is KE. Since energy is
conserved, set PE = KE or
. The mass cancels out and,
since the question asks for the approximate speed, g = 10 will suffice. 2 ×
10 × 5 = v2 and 100 = v2, so v = 10.
5. D
Work = Force × Distance or 2000 × 5 = 10,000 J.
6. C
To calculate power, start by determining the work performed. Since
there are 20 parts that weigh (exert a downward force) 10 N each that
are li ed 2 m, work = 20 × 10 × 2 = 400 J. The machine accomplishes this
work in 2 seconds. Power is
, or 200 watts.
7. D
Pressure is force divided by the area over which it is applied, so
8. C
This could be solved with two different approaches. Gear A makes 14
revolutions and has 15 teeth, so 14 × 15 = 210 teeth would pass any
point. Since gear B has 10 teeth, it would need to make 21 revolutions to
match the teeth of gear A. Alternatively, the gear ratio is 3:2, so the
proportion
could be used to obtain the same answer,
21.
9. B
The mechanical advantage of a wheel and axle is equal to the ratios of
the radii of the two wheels. The problem states that the smaller wheel’s
diameter is
m, so its radius is
m and the ratio of the two radii is
10:1.
10. A
The cross-section of a kitchen knife is very small on the cutting side and
gets thicker toward the top, just as a wedge does.
11. D
Torque (τ) is determined by multiplying a force (F) by the lever arm
length (r) that the force is acting through or τ = rF. In this case, to
achieve an applied torque of 50 -lb, with a 2 lever arm, where F =
= 25 lb of force is needed.
,
12. A
Based on Newton’s second law, F = ma, where F = force in newtons, m =
mass in kilograms, and a = acceleration in m/s2. Therefore, rearranging
the equation for mass, you get: m = . Since you know that friction is
not negligible, you also know that the resultant force will be less than 10
N (see diagram below). Therefore, the maximum mass possible in a
frictionless system is calculated by dividing 10 N by 10 m/s2, which gives
1 kg. Knowing that friction will diminish the applied force, the resulting
mass has to be less than 1 kg, which matches answer choice (A).
Resultant Force = 10 N – force of friction
Thus, the resultant force will be less than 10 N.
13. D
Kinetic friction is exhibited when surfaces/objects move past one
another. The normal force, which is a factor of the weight of the object,
will affect friction (for example: move your hand across a table lightly
and then again with more force; increased force leads to increased
friction). The nature and area of the surfaces in contact with each other
will also affect the friction that develops between two surfaces (for
example: moving your hand across a desk with oil on it is a lot easier
than with honey; also, moving one finger across a desk develops less
friction than moving your entire hand). The speed at which the surfaces
move past each, other however, does not impact the frictional forces
(though more heat may be generated).
14. D
Weight = gm, where g = gravitational acceleration (m/s2) and m = mass in
kg. On Xendor, the gravitational acceleration is 3 times as much as on
Earth, giving a new g of approximately 30 m/s2. To calculate weight on
Xendor, multiply the new gravitational acceleration by the person’s
mass: Weight = 30 m/s2 × 100 kg = 3000 N.
15. C
Recall that W = Fd, where W is work in joules, F is force in newtons and d
is distance in meters. Therefore, rearranging the equation for force, you
get: F =
. Taking 80 J and dividing by 2 m, you get 40 N.
MECHANICAL COMPREHENSION PRACTICE SET 2
16. C
The object remains at rest, so the acceleration is 0 and the net force
must also be 0. Given that the object is not moving, the frictional force
must be static rather than kinetic. The calculated force of static friction
is actually the maximum that can be attained without creating
movement. In this instance, not enough information is available to
determine if this maximum has been reached. However, since the object
remains at rest, the applied force must be equal to the force of static
friction.
17. C
Total mechanical energy is conserved as the ball moves down the hill,
meaning that the potential energy at the top will be converted to kinetic
energy at the bottom. To solve for the velocity at the bottom, the
potential energy must be set equal to the kinetic energy. Algebraically,
this can be written as
which simplifies to
by canceling out mass. Solving for velocity,
. Finally,
plugging in the values from the question stem and using 10m/s2 as an
approximation for g,
, so the velocity of
the ball when it reaches the bottom of the hill is 20 m/s.
18. A
The question gives the mass of the object in grams, so the mass must
first be converted to kg by dividing by 1,000, giving 0.5 kg. Then the
mass must then be converted into a force by multiplying by g (use 10
m/s2 for simplicity), so the weight of the mass is 0.5(10) = 5 N. Since the
mass is not accelerating, the total tension must be equal and opposite to
the weight of the object. Algebraically, this means T1 + T2 = 5 N. The
tensions are equal because the ropes are of equal length, they are
attached to the block in a symmetric fashion, and the mass of the block
is uniformly distributed. So T1 = T2 and 2T1 = 5 N, so T1 = 2.5 N.
19. B
Since the pressure is the same throughout a closed hydraulic system
and force is equal to pressure times the area over which it is applied, F1
must be greater than F2. Also, the work (force times distance) must be
equal on both sides. Since F1 > F2, it follows that d2 > d1.
20. C
Since the system is in rotational equilibrium, the net torque on the
system must be 0, so the torques exerted by the le - and right-hand
sides of the fulcrum must be equal. The question is asking the distance
from the 10 kg weight; let that distance equal x, so the distance between
the fulcrum and the 20 kg weight must be 9 − x. Setting the torques
equal to each other: 10xg = 20(9 − x)g. Gravity is on both sides of the
equation, so it will cancel out, giving 10x = 180 − 20x. Solving for x, x = 6
m.
21. B
The equation for kinetic energy is
. Since the weight of the object
was given, not the mass, the first step is to calculate the mass. W = mg,
so the equation can be rearranged to
in order to calculate the
mass. Given the weight of 98 N, it will be more accurate to calculate the
mass using g = 9.8 m/s2 rather than the approximation of 10 m/s2. So the
mass is
. Finally, the mass and velocity can be plugged into
the equation for kinetic energy:
.
22. B
Since power is work per unit of time and work is force times distance,
then
. Substituting the known values from the question,
. Note that the mass of the block was not
needed to answer this question. Recognizing and discarding extraneous
information is a skill that takes practice but is very helpful.
23. D
The first step is to convert the mass given into a force, which will be its
weight. The force of the weight is
. Since there are 4 pulleys, the
mechanical advantage is 4:1, meaning that
of the force can be applied
over 4 times the distance to pull up the mass. Since the weight is 1,000
N, the force applied would be 250 N.
24. A
Pressure is equal to force divided by the area over which it is applied.
The force is equal to the weight of the woman. To calculate the area,
multiple the dimensions of the snowshoes, so
inches. Since she is wearing two shoes, the total area is
square inches. Divide the force by the area:
square
.
25. D
The normal force must be equal and opposite to the force exerted by the
block on the table in accordance with Newton's third law of motion.
Since the mass of the object is given in kg, the weight must first be
calculated using the formula w=mg to get a weight of 400 N. There is
also a force applied downward on the block of 100 N, so the total force
exerted on the table is 500 N. Since the object remains at rest, the
normal force must be equal to 500 N to get a net force of 0 and have no
acceleration.
26. D
The fact that the ball was thrown at an angle may seem to complicate
the problem. The ball will travel outward and upward until it reaches its
maximum altitude, then begin to travel downward and outward.
However, since the question does not specify the direction that the ball
is traveling when it hits the ground, the problem can be solved by
considering that the total kinetic energy when the ball finally reaches
the ground will be the sum of the initial kinetic energy and the potential
energy that is converted to kinetic energy. Since air resistance is
minimal, no kinetic energy will be lost to air resistance. The potential
energy will initially be equal to mgh. Substituting the known numbers
and using the approximation of 10 m/s2 for g, you get 5(10)(10) = 500 J.
To calculate the beginning kinetic energy, use the equation
. Substituting the numbers from the question stem, we
get
or 250 J. Summing the two forces gives 750 J.
27. C
Tools do use the principles of mechanics but measuring devices do not.
Similarly, machines that transmit or use energy are governed by these
principles, but the study of mechanics is not limited to machines. While
trajectories are a type of motion, the more broad category of "motion" is
the proper answer.
28. C
Since the coefficient of static friction is greater than that of kinetic
friction, once sufficient force is applied to overcome the maximum value
of the force of static friction, there will be a net force acting to move the
object. Because of Newton's second law, F = ma, a non-zero net force
always creates a non-zero acceleration. That formula applies to the net
force, not any force that “accumulates.” As the object's velocity
increases, so will its momentum, but this is an effect of the acceleration,
not the cause.
29. A
In order for the brothers to be balanced, the torque (rotational force)
exerted by each boy must be equal. The little brother sits 8 feet from the
fulcrum and weighs 75 pounds, so the torque he creates is
. In order for the big brother to generate 600
-lb. of torque, he should sit 6 feet from the center of the seesaw, since
.
30. D
Since force equals pressure times the area over which the pressure is
applied and the pressure is the same throughout the system, the ratios
of the forces will be equal to the ratio of the areas of the two pistons.
The radius of the smaller piston is 1 cm and that of the larger piston is 10
cm, so
. Cancel the
N.
REVIEW AND REFLECT
and cross-multiply to get F = 2,000
How did you do on this practice set? As you review your work, ask yourself
some questions:
Did you remember the equations you learned in the chapter?
Did you think about how various forces were at work in the practice
questions?
Did you stop to think carefully about what the question is asking for,
simplify or solve, and then make a prediction before looking at the
choices?
Want more practice with Mechanical Comprehension? Log in at
kaptest.com/login to try more questions in the Qbank.
CHAPTER 14
ASSEMBLING OBJECTS
Know What to Expect
The ASVAB analyzes your abilities and aptitude to help you discover what
military careers would be the best match for you. For example, pilots,
mechanics, machine operators, and engineers need to develop good
spatial relationship skills—that is, the ability to see how parts will look
when assembled into a whole. The Assembling Objects (AO) subtest
examines your spatial relationship skills, so it gives you an opportunity to
show that you are good at putting things together. As always, we
recommend checking with your recruiter or career counselor to learn more
about which subtests will be important to you in reaching your goals.
The skills required for the AO test are learnable. Even test takers who
struggle to visualize how shapes fit together can greatly improve their
spatial relationship skills by learning strategies and practicing. In this
chapter, you’ll have the opportunity to do just that.
The CAT-ASVAB test includes 15 AO questions, with a time limit of 17
minutes. Remember, unlike the paper-and-pencil ASVAB, you will not be
able to review or change an answer once you submit it. The paper-andpencil ASVAB includes 25 AO questions, with a 15-minute time limit.
The Assembling Objects subtest contains two types of test items. We’re
going to call these:
Jigsaw-Puzzle-Type Problems, which test your ability to choose how
an object will look when its parts are put together into a larger shape.
Connector-Type Problems, which test your ability to correctly connect
two objects with a line at the indicated points.
In both types of AO items, you are offered five boxes. The le most or first
box contains drawings of unconnected parts. The four answer-choice boxes
hold drawings of shapes, only one of which shows the shape that would
result when all the parts are correctly assembled.
Jigsaw-Puzzle-Type Problems
Learning Objectives
In this section, you will learn to:
identify what your task is on Jigsaw-Puzzle-Type problems
apply the Kaplan Method for Assembling Objects questions to JigsawPuzzle-Type problems
Study the question below.
Which figure best shows how the objects in the left box will
appear if they are fit together?
Every AO question has a box on the very le that shows a number of individual
parts. Let’s call that box on the le the instructions box. Each AO question then
offers four answer choices. Three of those choices distort the shapes in the
instructions box. Only one of them accurately shows how the shapes would fit
together into a whole. In this case, (C) is correct.
Having trouble visualizing why (C) is correct? Study the diagram below.
However, you do not have to visualize assembling the parts in your head in order
to answer AO questions. (That’s good news.) Rather, approach these questions
strategically. Did you notice that each of the answer choices in the example above
is a circle dominated by a large triangle? That will be helpful. Now, focusing on
the circle outline won’t be helpful, because it’s the same in all four choices.
However, the placement and shape of that large triangle varies among the
answer choices. Thus, focusing on that prominent triangle will help you eliminate
some choices right off the bat. You can call that key shape a landmark, in the
sense that it helps you find what you’re looking for.
What do you notice about the triangle depicted in the instructions box? It’s a right
triangle, or very close to being a right triangle. How many of the answer choices
clearly do not have right triangles? (A) and (D). Cross them off. Your landmark just
knocked out half the choices.
Only (B) and (C) remain as possible choices. Find another key trait in the
instructions box. Here, counting the number of shapes might be helpful. There
are four shapes in the instructions box. How many shapes do (B) and (C) have? (B)
has only three, so it can’t be right. Circle (C) and move on to the next question.
Here’s a method you’ll use on all Assembling Objects questions. Memorize this
method now, so that you can work on mastering it in your practice.
THE KAPLAN METHOD FOR ASSEMBLING OBJECTS
QUESTIONS
Step 1: Identify a landmark in the instructions box.
Step 2: Eliminate any answer choices that don’t display the landmark.
Step 3: Compare other shapes to eliminate remaining choices.
Study the example below.
Question
Which figure best shows how the objects in the le box will appear if they are fit
together?
Analysis
Step 1: The easiest landmark here might be the smallest shape, which looks like a
small pizza slice.
Step 2: (C) and (D) don’t have that small pizza shape, so they’re out. (A) has a
similar shape, but it’s far too big. So (A) is out as well. (B) is correct.
Step 3: No need to compare other shapes here.
In Step 1, your landmark shape in Jigsaw-Puzzle-Type AO problems might be:
the largest shape
the smallest shape
the shape that seems to differ the most among the answer choices
the most oddly-shaped piece
a shape with a recognizable angle or side (such as a right angle, or a steeply
curved side)
With practice, you will learn to efficiently spot a useful landmark in the
instructions box.
When you get to Step 3, here are strategies you can use to eliminate any
remaining wrong answer choices:
Count the number of parts. If you are taking the paper-and-pencil test, you can
actually assign each part a number and write it in.
Find a second landmark. If you used the largest shape in Kaplan Method Steps
1 and 2, perhaps you would use the smallest shape as your second landmark.
Compare the sizes of the shapes in the instructions box to the remaining
choices.
And here are some things to watch out for in wrong answer choices on JigsawPuzzle-Type AO questions:
You can expect one or more of the shapes in the instructions box to be inverted
le -to-right or top-to-bottom in one or more of the wrong answer choices. The
correct answer might move the parts around or rotate them, but it won’t invert
any of them.
An enlarged or shrunken version of a shape in the instructions box might
appear in the wrong answer choices. The correct answer will have the same
shapes in the same sizes.
A shape that has all straight edges in the instructions box may have a curved
edge in some wrong answer choices.
A shape from the instructions box may be carved into two or more smaller
shapes in some wrong answer choices.
Try these problems on your own, and then read the explanations below.
Which figure best shows how the objects in the left box will
appear if they are fit together?
Which figure best shows how the objects in the left box will
appear if they are fit together?
Explanations
Note: It’s perfectly fine if you chose different landmarks than the ones below, as
long as you were able to work efficiently through the questions.
1. Step 1: The instructions box has two shapes that look like fat square brackets;
those are good landmarks.
Step 2: (B) doesn’t have two of those shapes; eliminate. (C) has two but they’re
too long; eliminate. Only (A) and (D) remain.
Step 3: Count the number of pieces in the instruction box: there are five. (D) has
three shapes; eliminate.
(A) is correct.
2. Step 1: The instructions box has an odd shape that looks like a pie piece with
two branches growing out of the narrow end; that’s a good landmark.
Step 2: (A) and (C) have no such piece; eliminate. (B) and (D) remain.
Step 3: The instructions box has four shapes; (B) has five. Eliminate (B).
(D) is correct.
Connector-Type Problems
Learning Objectives
In this section, you will learn to:
identify what your task is on Connector-Type problems
apply the Kaplan Method for Assembling Objects questions to
Connector-Type problems
Study the example below.
Which figure best shows how the objects in the left box will
touch if the letters for each object are matched?
The instructions box of a Connector-Type problem displays two geometric
shapes. Some problems have familiar shapes such as circles, squares,
rectangles, and triangles, while others have more unusual shapes such as
letters, clouds, or hearts. The instructions box will also display a connector line.
You could think of the connector line as being a string you must tie to the two
shapes in precisely the places indicated.
The two shapes and the connector line are labeled with dots and small letters to
indicate points where you are to connect the shapes. You will see one dot on
each shape, each labeled with a letter. Dots on the ends of the connector line
will correspond to these letters. Sometimes the dots will be on the edges of
shapes, and sometimes they will be inside the shapes.
You are asked to attach the two shapes to the line at the correct points, based
on the diagram in the instructions box. The shapes may be rotated in the
solution boxes, but the correct solution cannot be flipped. In the example
above, choice (D) is correct.
Having trouble seeing it? Study the diagram below.
However, just as with Jigsaw-Puzzle-Type questions, you do not need to be able
to visualize the solution in your head. The Kaplan Method works on ConnectorType problems just as it does on Jigsaw-Puzzle-Type problems. Study the
example below.
Question
Which figure best shows how the objects in the left box will
touch if the letters for each object are matched?
Analysis
Step 1: A good landmark here is the fact that dot a is in the middle of the
straight side of the semicircle in the instructions box.
Step 2: Choices (B) and (D) don’t display the correct placement of connection a;
eliminate. Only (A) and (C) remain.
Step 3: A second landmark could be the placement of connection b: it’s on a
corner of the rectangle. Choice (C) places it wrongly in the middle of one side of
the rectangle. (A) is correct.
In Step 1, your landmark in Connector-Type AO problems might be:
whether a dot is placed in the middle of a side or on a corner of a shape
whether a dot is placed on the edge or inside a shape
a shape itself
With practice, you will learn to efficiently spot a useful landmark in the
instructions box. If you are testing on paper and pencil, you could actually add
the labels a and b to the answer choices in order to help you eliminate choices
that don’t display your landmark.
When you get to Step 3, here are strategies you can use to eliminate any
remaining wrong answer choices:
Find a second landmark. If you used dot a as your first landmark, you might
use dot b as your second landmark.
If a dot is placed on the corner of a shape in the instructions box, check to see
which corner is attached to the connector line in the answer choices.
Check to see if any of the shapes have been flipped or inverted in the answer
choices.
Here are some things to watch out for in wrong answer choices on ConnectorType AO questions:
If the connection point is on the edge of a shape in the instructions box, it
may appear inside the shape in some wrong answer choices (or vice versa).
If the connection point is on the corner of a shape, expect it to either appear
on other corners in some of the wrong answer choices or appear in the
middle of an edge in some wrong answer choices.
One or more of the shapes in the instructions box may be inverted le -toright or top-to-bottom in one or more of the wrong answer choices.
An enlarged or shrunken version of a shape in the instructions box might
appear in the wrong answer choices. The correct answer will have the same
shapes in the same proportions.
Try it on your own, and then review the explanations below.
Which figure best shows how the objects in the le box will touch if the letters
for each object are matched?
Which figure best shows how the objects in the le box will touch if the letters
for each object are matched?
Explanations
Note: Your landmarks may differ. That’s fine, as long as you were able to work
through the problems efficiently and accurately.
1. Step 1: Dot b looks like a good landmark: it’s on the narrowest point of the
triangle.
Step 2: Choice (C) places the connector on a different corner of the triangle, and
choice (D) places it in the middle of the triangle. Eliminate. (A) and (B) remain.
Step 3: A good second landmark would be the placement of dot a: it’s in the
middle of the three-lobed shape. Choice (A) wrongly places it on the edge.
Choice (B) is correct.
2. Step 1: The instructions box includes a shape that looks like a hair dryer, and
dot a is at the point where the trigger of the hair dryer meets the barrel of the
hair dryer. That’s a good landmark.
Step 2: Choices (A) and (B) misplace the connection point on the hair dryer;
eliminate. (C) and (D) remain.
Step 3: The circle with dot b is the same in choices (C) and (D), so a different
landmark needs to be used. Instead, compare the hair dryers: turns out it’s
flipped in choice (C).
Choice (D) is correct.
Assembling Objects Practice Set 1
For each question, select the answer that best shows how an object will
look when its parts are put together. This practice set has 15 questions,
which is the number of Assembling Objects questions you will see if
you take the CAT-ASVAB.
1.
(A)
(B)
(C)
(D)
2.
(A)
(B)
(C)
(D)
3.
(A)
(B)
(C)
(D)
4.
(A)
(B)
(C)
(D)
5.
(A)
(B)
(C)
(D)
6.
(A)
(B)
(C)
(D)
7.
(A)
(B)
(C)
(D)
8.
(A)
(B)
(C)
(D)
9.
(A)
(B)
(C)
(D)
10.
(A)
(B)
(C)
(D)
11.
(A)
(B)
(C)
(D)
12.
(A)
(B)
(C)
(D)
13.
(A)
(B)
(C)
(D)
14.
(A)
(B)
(C)
(D)
15.
(A)
(B)
(C)
(D)
Assembling Objects Practice Set 2
For each question, select the answer that best shows how an object
will look when its parts are put together. This question set has 15
questions, which is the number of Assembling Objects questions
you will see if you take the CAT-ASVAB.
16.
(A)
(B)
(C)
(D)
17.
(A)
(B)
(C)
(D)
18.
(A)
(B)
(C)
(D)
19.
(A)
(B)
(C)
(D)
20.
(A)
(B)
(C)
(D)
21.
(A)
(B)
(C)
(D)
22.
(A)
(B)
(C)
(D)
23.
(A)
(B)
(C)
(D)
24.
(A)
(B)
(C)
(D)
25.
(A)
(B)
(C)
(D)
26.
(A)
(B)
(C)
(D)
27.
(A)
(B)
(C)
(D)
28.
(A)
(B)
(C)
(D)
29.
(A)
(B)
(C)
(D)
30.
(A)
(B)
(C)
(D)
Answers and Explanations
ASSEMBLING OBJECTS PRACTICE SET 1
1. A
Shape #3 has an unusual shape, so it is a good landmark; it is a fairly
long arc of the outer circle defined by two lines that meet in an obtuse
angle. This shape appears only in choice (A). The shape at the le side of
choice (C) is similar, but the long and short legs are reversed. Since only
one answer choice contains this shape, there is no need to select a
second shape other than to verify the correct answer.
2. B
Shape #5 is the most distinct, since it is a triangle and the others are
quadrilaterals. This landmark shape can be found only in choice (B). The
tall triangle in choice (D) might be tempting, but the longest leg of this
triangle is on the right side whereas the longest leg of the correct shape
is on the le side. Since the three incorrect choices have been
eliminated, there is no need to check a second shape.
3. D
Shape #1 is large and has a distinct shape, so select that as your
landmark. Checking the answers, #1 can be found in choice (D). The
shape at the top of choice (A) is similar, but it "points" the wrong
direction (it is flipped over). Again, there is no need to select a second
shape to analyze
4. C
Since shape #4 is the only triangle and closely resembles an equilateral
triangle, start with that shape as the landmark. Then, since there are
similar-looking triangles in both choices (C) and (D), shape #3, which is
much smaller than either of the other remaining choices, would be a
suitable second shape to examine. Shape #3 is replicated in choice (C),
but the corresponding quadrilateral in choice (D) is a mirror image of the
original shape. Remember that shapes can be rotated in the plane to
change their placement, but they cannot be rotated about an axis.
Therefore, a shape that is inverted top to bottom or le to right will not
be part of the correct answer choice.
5. A
A quick glance at the shapes shows that the "point" sticking out of
shape #3 must fit into the "notch" in shape #4 and that if #4 is on top,
the notch will be on the lower right side of #4. Thus, the combination of
these two shapes can serve as a landmark. The correct combination
occurs only in choice (A). Although these two pieces are nested with the
notch pointed up in the other choices, none of the alternatives have the
"point" in the lower right-hand corner.
6. C
Shape #1 looks unique and should be a good landmark but,
unfortunately, only choice (D) does not contain that shape. Shape #4 is
the most complex of the remaining shapes. While there is a trapezoid in
choice (A), that one is not long enough and it is flipped. The trapezoid in
choice (B) is reversed. The trapezoid in (C) is, indeed, shape #4 turned
90° clockwise.
7. B
Shape #1 is large and easily identifiable, making it a good landmark.
However, it appears in all four answer choices. Shape #3, a "bloated
check mark," appears in choices (A) and (B) (it is also in (C), but it is
flipped there). Therefore, another shape must be examined. Shape #4
does not appear in choice (A), so choice (B) is correct.
8. A
Shape #1 is the largest, so select that as the landmark since it should be
easily identifiable in the answer choices. In choices (B) and (D), the "L" is
backward, so eliminate those answers. Shapes #2 and #5 are distinct, so
they could be examined next. Since neither one appears in choice (C),
the correct answer is (A).
9. C
Dot b is a good choice for the landmark because it is located near, but
not at, one end of the oval. Dot a, on the other hand, is at one of 5 points
on the star. Using dot b, you can eliminate choices (A) and (B)
immediately. Choice (D) requires more careful examination. If the initial
oval shape were rotated 180° so that the dot were near the bottom, the
dot would then be on the le side. However, the connector line ends at
the right side of the oval, so (C) is correct.
10. A
The shape on which dot a is placed is a good landmark because the
arrow lets you easily compare the orientation of the shape as well as the
location of the connector line. The connector line in choice (C) touches
the corner of the shape with dot a rather than the middle of a short side.
If the shape is rotated so that the arrow points up, then dot a is on the
le , making choices (B) and (D) wrong. Choice (A) is correct.
11. D
The triangle appears to be a right triangle, and dot b is located on the
longer leg near the end closest to the short leg, so this should be a good
landmark. In choices (B) and (C), the connector line terminates on the
hypotenuse of the triangle, so eliminate those answers. In choice (A), the
connector line does end on the long leg of the triangle, but at a point
that is closer to the acute angle. In choice (D), the dot is at the correct
location on the triangle, and a quick double check verifies that the
connector line is at the proper place on the other shape; choice (D) is
correct.
12. C
Dot a, on the straight edge near the corner of the "D," is easy to spot, so
use that for the initial landmark. If the "D" is rotated 180°, the dot moves
to the top right, so answer choice (A) is incorrect, but (B) is still in the
running. If the "D" is rotated 90° or 45° counterclockwise, as in (C) and
(D), respectively, the dot is at the bottom right, so choice (C) is correct
for this shape but (D) is eliminated. The flattened, six-pointed star shape
has an asymmetry that can be used. If you rotate the object so that its
longest axis is horizontal, dot b is on either the upper right prong or the
lower le prong, depending on the orientation. If the figure in choices
(B) and (C) is aligned horizontally, the connector in (B) touches the
wrong prong—either the upper le or the lower right, depending on the
orientation. The connector in choice (C) touches the upper right prong,
making this the correct answer.
13. C
Although the cloud is an intriguing shape, it might be easier to pinpoint
the connector line location on the simpler diamond shape, so you could
try using dot a as the initial landmark. Unfortunately, all the answer
choices except (A) correctly place the connector line on the diamond, so
it's on to dot b. Choice (D) connects at or near the end of the cloud, but
dot b is in the middle of the "puffier" side of the cloud. In choice (B), the
dot appears to be too close to one end of the cloud and, moreover, it
connects to the less puffy side. Choice (C) is correct.
14. A
Dot a, located approximately midway along the longest side of the
reverse "L," should be a good landmark. In choices (B) and (D), the line
connects to the shorter side of the shape, so eliminate those answers. In
choice (C), the line connects to the proper side but too close to the end.
Choice (A) is correct.
15. C
Since its shape is a bit more complex, with a line inside of a circle, use
dot b for the landmark. Eliminate choice (B) since the connector line
terminates in the middle of the circle. The other choices place the end of
the connector correctly in the circle. The analysis of dot a will be more
involved. In choice (A), the banner shape has been rotated
approximately 45° counterclockwise, so the correct point is the le most
corner of the banner rather than the bottom one. Look closely at the
banner in choice (D). It could be rotated approximately 150°
counterclockwise or 210° clockwise in order to be oriented as shown.
However, the curved part closest to the circle would then be convex
(curved outward) in the direction of the hole. In choice (D), however,
that part of the banner is concave (curved inward), so (C) is correct.
ASSEMBLING OBJECTS PRACTICE SET 2
16. D
Shape #2, which looks like an oblong about to devour something, is
certainly the most distinctive choice for a landmark. In choice (A), the
oblong has become a circle, so that answer is out. In choice (B), the long
and short "jaws" are reversed. The shape in choice (C) looks
suspiciously thin, but pick another shape to test, just to be certain.
Shape #1, a symmetrical-looking curve and chord, is no longer
symmetrical in choice (C), so (D) is the correct answer.
17. A
Shape #2 is certainly an oddball, making it a good landmark. At first
glance, it might appear that this shape is in choice (C), but notice that it
has been split at the top. This means that choice (C) has five pieces,
which is another reason to eliminate it. Since shape #2 does not appear
at all in choices (B) or (D), the correct answer is (A), with shape #4 nested
snugly inside shape #2.
18. C
The shapes are all fairly simple in this problem; #2 would be one option
to start with as a landmark. That shape clearly is missing from choice
(A). Choice (B) might be tempting, but the sloping side is reversed.
Choice (D) has a shape similar to #2 pointing down, but it is much too
large, so choice (C) is correct. To double-check, note that shape #3 does
not appear in choice (D).
19. B
Shape #1, which looks like the dot-gobbler from an old video game, is an
easy shape to use as a landmark. Since that shape is absent (or
distorted) in choices (A), (C), and (D), eliminate those answers. Shape #1
is found at the right end of choice (B), rotated 90° counterclockwise, so
that is the correct answer.
20. D
Shape #2 is the only one without a curved side, so that is a good
landmark. That shape is not present in choices (A) and (C), so eliminate
those and select another shape for a second search. Shape #1 is the
most complex remaining shape. Although there is a similarly shaped
piece in the lower half of choice (B), that shape is larger than the
original, so choice (D) is correct.
21. C
Shape #1 is the largest and most complex, so it is a logical landmark.
The notch at the corner of what otherwise would look like a right
triangle should be easily identifiable. The notch is missing in choice (B)
and is in the wrong corner of the shape in choice (D), so eliminate those
two answers. Shape #2 is a readily recognizable choice for the second
scan. That shape cannot be found in choice (A), so choice (C) is the
correct answer.
22. A
Shape #1 is unique, since the other three shapes are triangles. Use that
one as the landmark. In choice (C), the "L" doesn't have the slanted end
on the short leg, so eliminate that answer immediately. A careful
inspection of choices (B) and (D) reveals that the legs of the "L" are
reversed; eliminate those answers. Answer choice (A) is correct.
23. C
Shape #3 is the most complex of the group and is a good choice for a
landmark shape. While the corresponding shape in choice (A) is similar,
the long and short sides are reversed. In choice (B), the original six-sided
shape has morphed into a seven-sided shape. Shape #3 is present in the
remaining answers, so shape #4, another complicated shape, could be a
good option for the second scan of the remaining choices.
Unfortunately, very similar shapes are found in both choices (C) and (D).
Shape #1, however, is missing from choice (D), so choice (C) is correct.
24. B
Dot a, which is situated at the vertex of the short leg and apparent
hypotenuse of the triangle, is a good landmark. The connector line only
touches the smaller triangle at that point in choice (B).
25. C
The shape that shows dot b is an irregular hexagon; dot b is located at
the intersection of a long side and a short side of that hexagon. Once
again, you don't need a second landmark to solve this one, since the
connector line only touches the hexagon at dot b in choice (C).
26. D
Dot a is attached to the "racetrack" shape at the end of the backstretch
and can serve as the landmark. The connector line does not meet the
"racetrack" at the proper point in choices (B) and (C). Dot b is placed
very close to the corner of the square. In choice (A), the connector line is
at the corner of the square, so choice (D) is correct.
27. A
The egg is a nice simple shape, whereas the star is just slightly
elongated; analyzing the connection to the star could be more difficult.
Therefore, start with dot b, located just inside the egg, as the landmark.
Since choices (C) and (D) show the connector line touching the outside
of the egg, those choices can be eliminated. Now look at the connection
to the star. In both (A) and (B), the connector touches the star at an inner
vertex. However, in (B) the connection is in the middle of the “longer” or
more stretched out side of the star. Therefore, choice (A), which makes
the connection on the “narrow” end, is correct.
28. C
While dot b is located on the more complex of the two shapes, dot a has
the readily identifiable feature of being linked to the outside of the circle
by a short line rather than just "floating" inside the circle. Thus, dot a is
a good starting landmark, and only choice (C) shows this. Had you
chosen to use dot b as the landmark, you could have eliminated choice
(B) because the odd shape is flipped (if it were upside-down, the long
“finger” would be on the right, not the le ) and then proceeded to
answer the question using dot a.
29. D
Since it is attached to a more complex shape, use dot b as the landmark.
In choice (A), the shape would have to be flipped rather than rotated to
be oriented in that manner. The shape is proper in choice (C), but the
connector line touches the shorter of the two straight lines. Look at dot
a to decide which of the two remaining choices is correct. Although the
connector line correctly touches the vertex of the smallest angle of the
triangle in choice (B), just as was the case when analyzing dot b, the
triangle would have to be flipped rather than rotated to appear as it
does. Choice (D) is correct.
30. A
Since one corner of the rectangle is notched, dot a, which is at the
opposite end of the long side of the rectangle, is a good landmark. In
choice (B), the connector line touches the rectangle at the corner that is
separated from the notch by the shorter side of the rectangle. Choice (C)
reverses the notched and unnotched corners, so eliminate choice (C) as
well. Now use dot b to eliminate one more wrong answer. In choice (D),
the "O" has been rotated to be "upright," so dot b is along the upper
right side of the double oval. However, the line connects at the lower
right. Choice (A) is correct.
REVIEW AND REFLECT
How did you do? Which questions were more challenging? How could you
improve your choice of landmarks? Going over the questions again may
prove helpful.
Want more instruction and practice with Assembling Objects? Log in at
kaptest.com/login to watch the video instruction in this book's online
resources and try more questions in the Qbank.
CHAPTER 15
ASVAB PRACTICE TESTS
On the following pages, there are two full-length practice tests with
complete answers and explanations. The number of questions and timing
follow the ASVAB's paper-and-pencil format. Do your best to mimic the
Test Day scenario. Take the test in a quiet location, do not use a calculator,
and stick to the time frames allotted for each section.
When you’re done, review the explanations to determine why the right
answers are right and the wrong answers are wrong.
For experience taking a test on the computer, log in to your online
resources at kaptest.com/login. If you haven’t yet registered your book,
see “Welcome to Your ASVAB Studies” toward the front of this book for
registration instructions.
ASVAB PRACTICE TEST A
ASVAB PRACTICE TEST A
Part 1: General Science (GS)
11
Minutes
— 25
Questions
Directions: In this section, you will be tested on your knowledge of
concepts in science generally reviewed in high school. For each
question, select the best answer and mark the corresponding oval
on your answer sheet.
1. A genus classification contains several related
(A) species
(B) families
(C) orders
(D) phyla
2. Particles that orbit the nucleus of an atom are
(A) anions
(B) electrons
(C) positrons
(D) photons
3. As a human breathes, air is first warmed and filtered in the
(A) trachea
(B) pharynx
(C) oral cavity
(D) nasal cavity
4. In the food chain described below, which is the tertiary consumer?
dandelion → rabbit → fox → coyote
(A) dandelion
(B) rabbit
(C) fox
(D) coyote
5. The process by which a solid becomes a gas is known as
(A) boiling
(B) sublimation
(C) melting
(D) diffusion
6. The gravitational force the Moon exerts on the Earth is
(A) less than one-half as much as that exerted by the Earth on the
Moon
(B) one-half as much as that exerted by the Earth on the Moon
(C) the same as that exerted by the Earth on the Moon
(D) more than that exerted by the Earth on the Moon
7. Fungi are organisms that break down dead matter and return the
organic material back into the environment for reuse. They are
examples of
(A) producers
(B) decomposers
(C) consumers
(D) mutualists
8. What is the freezing point of water in Kelvin?
(A) −273 K
(B) 0 K
(C) 100 K
(D) 273 K
9. Tough elastic tissues found in the joints that connect bones to
bones are called
(A) ligaments
(B) tendons
(C) cartilage
(D) muscles
10. Stress, a poor diet, cigarette smoking, and hereditary factors all
contribute to individuals developing
(A) diarrhea
(B) high blood pressure
(C) gall stones
(D) anemia
11. Which clouds are thin and wispy and occur high in the atmosphere?
(A) cirrus
(B) cumulus
(C) stratus
(D) stratocumulus
12. Fossils are most likely to be found in which of the following types of
rock?
(A) igneous
(B) metamorphic
(C) sedimentary
(D) volcanic
13. Animals that consume only plants are called
(A) saprophytes
(B) herbivores
(C) carnivores
(D) omnivores
14. What type of star is the Sun?
(A) red dwarf
(B) blue giant
(C) white dwarf
(D) yellow dwarf
15. Which of the following is a group of organisms of the same species
living in the same region?
(A) biome
(B) ecosystem
(C) community
(D) population
16. Which one of these planets is NOT an outer planet?
(A) Jupiter
(B) Saturn
(C) Uranus
(D) Earth
17. A boulder that begins to roll down a hill is an example of an energy
conversion from
(A) potential to thermal
(B) potential to kinetic
(C) kinetic to thermal
(D) kinetic to potential
18. The lowest layer of the Earth’s atmosphere is called the
(A) ionosphere
(B) mesosphere
(C) stratosphere
(D) troposphere
19. According to the law of conservation of energy
(A) energy is the capacity to do work
(B) energy can neither be created nor destroyed
(C) energy is possessed by a moving object
(D) energy is stored in an object as a result of its position, shape,
or state
20. As an ambulance passes, its pitch seems to change. This perception
is best explained by
(A) convection
(B) Newton’s third law
(C) the Doppler effect
(D) momentum
21. A concave lens is also known as a
(A) focal point
(B) converging lens
(C) convex lens
(D) diverging lens
22. The smallest particle of a covalent compound that can exist in a
free state and still retain the characteristics of that compound is
a(n)
(A) proton
(B) quark
(C) atom
(D) molecule
23. Which of the following is most responsible for oceanic tides?
(A) the orbit of the Earth around its own axis
(B) the magnetic polarity of the Earth
(C) the orbit of the Moon around the Earth
(D) the orbit of the Earth around the Sun
24. In the Periodic Table of the Elements, the elements in a column are
referred to as a
(A) period
(B) group
(C) configuration
(D) unit
25. In a chemical change, the molecules that enter the reaction are
called
(A) reactants
(B) products
(C) compounds
(D) elements
IF YOU FINISH BEFORE THE TIME IS UP, YOU MAY CHECK
OVER YOUR WORK ON THIS PART ONLY.
STOP
ASVAB PRACTICE TEST A
Part 2: Arithmetic Reasoning (AR)
36
Minutes
— 30
Questions
Directions: In this section, you are tested on your ability to use
arithmetic. For each question, select the best answer and mark the
corresponding oval on your answer sheet.
1. Three apples cost as much as 4 pears. Three pears cost as much as
2 oranges. How many apples cost as much as 72 oranges?
(A) 36
(B) 48
(C) 64
(D) 81
2. If 48 of the 60 seats on a bus were occupied, what percent of the
seats were NOT occupied?
(A) 12%
(B) 15%
(C) 20%
(D) 25%
3. Effin sings for $1,000 an hour. Her rate increases by 50% a er
midnight. If she sings one night from 8:30 p.m. until 1:00 a.m., how
much should she be paid?
(A) $4,500
(B) $5,000
(C) $5,500
(D) $6,000
4. Fran has a drawer containing 4 black T-shirts, 3 orange T-shirts, and
5 blue T-shirts. If she picks one T-shirt at random from the drawer,
what are the chances that it will NOT be orange?
(A)
(B)
(C)
(D)
5. A er a 5-hour flight from Newark, Harry arrives in Denver at 2:30
p.m. If the time in Newark is 2 hours later than the time in Denver,
what was the time in Newark when Harry began the flight?
(A) 10:30 a.m.
(B) 11:30 a.m.
(C) 3:30 p.m.
(D) 5:30 p.m.
6. A full box of chocolate contains 24 pieces. If Doris starts out with
198 pieces of chocolate, how many pieces will she have le over if
she fills as many boxes as she can?
(A) 3
(B) 6
(C) 8
(D) 10
7. If 75% of x is 150, what is the value of x?
(A) 150
(B) 175
(C) 200
(D) 250
8. Rachel’s average score a er 6 tests is 83. If Rachel earns a score of
97 on the 7th test, what is her new average?
(A) 85
(B) 86
(C) 87
(D) 88
9. A delivery service charges $25.00 per pound for making a delivery. If
there is an additional 8% sales tax, what is the cost of delivering an
item that weighs
of a pound?
(A) $20.00
(B) $21.60
(C) $22.60
(D) $24.00
10. A cake recipe requires
of an ounce of vanilla extract. How many cakes can be made
using a package containing 60 ounces of vanilla extract?
(A) 48
(B) 80
(C) 96
(D) 100
11. Ed has 100 more dollars than Robert. A er Ed spends 20 dollars on
groceries, he now has 5 times as much money as Robert. How
much money does Robert have?
(A) $16
(B) $20
(C) $24
(D) $30
12. 587 people are traveling by bus for a field trip. If each bus seats 48
people and all of the buses but one are filled to capacity, how many
people sit in the unfilled bus?
(A) 37
(B) 36
(C) 12
(D) 11
13. Riley brings 100 cookies to school for her class party. If there are 15
students in the class, including Riley, and there are 25 cookies le
a er the party, what is the average number of cookies that Riley
and her classmates ate?
(A) 1
(B) 4
(C) 5
(D) 6
14. A person 4 feet tall casts a 9-foot shadow at the same time that a
nearby tree casts a 21-foot shadow. What is the height of this tree,
in feet?
(A) 7
(B) 8
(C) 9
(D) 10
15. In a group of 25 students, 16 are female. What percent of the group
is female?
(A) 16%
(B) 40%
(C) 60%
(D) 64%
16. Phil is making a 40-kilometer canoe trip. If he travels at 30
kilometers per hour for the first 10 kilometers, and then at 15
kilometers per hour for the rest of the trip, how many more minutes
will it take him than if he travels the entire trip at 20 kilometers per
hour?
(A) 20
(B) 24
(C) 30
(D) 40
17. In a certain class, 3 out of 24 students are in student organizations.
What is the ratio of students in student organizations to students
not in student organizations?
(A)
(B)
(C)
(D)
18. In a certain baseball league, each team plays 160 games. A er
playing half of their games, team A has won 60 games and team B
has won 49 games. If team A wins half of its remaining games, how
many of its remaining games must team B win to have the same
number of wins as team A at the end of the season?
(A) 51
(B) 59
(C) 60
(D) 61
19. A vendor bought 10 crates of oranges for a total cost of $80. If he
lost 2 of the crates, at what price would he have to sell the
remaining crates in order to earn a total profit of 25% of the total
cost?
(A) $8.00
(B) $10.00
(C) $12.50
(D) $15.00
20. A machine labels 150 bottles in 20 minutes. At this rate, how many
minutes does it take to label 60 bottles?
(A) 2
(B) 4
(C) 6
(D) 8
21. 15 × (−5) =
(A) 10
(B) 75
(C) −75
(D) −225
22. Mike has a collection of baseball cards and baseball figurines. If the
ratio of cards to figurines is 5:7 and there are 25 cards in his
collection, how many figurines does he have?
(A) 20
(B) 35
(C) 40
(D) 45
23. Two hot dogs and a soda cost $3.25. If three hot dogs and a soda
cost $4.50, what is the cost of two sodas?
(A) $0.75
(B) $1.25
(C) $1.50
(D) $2.50
24. Danielle drives from her home to the store at an average speed of
40 miles per hour. She returns home along the same route at an
average speed of 60 miles per hour. What is her average speed, in
miles per hour, for the entire trip?
(A) 48
(B) 50
(C) 52
(D) 55
25. At a certain school the ratio of teachers to students is 1 to 10. Which
of the following could be the total number of teachers and
students?
(A) 100
(B) 121
(C) 222
(D) 1,011
26. The average of two numbers is equal to twice the positive
difference between the two numbers. If the larger number is 35,
what is the smaller number?
(A) 9
(B) 15
(C) 21
(D) 27
27. Each of seven runners on a relay team must run a distance of 1.27
kilometers. Approximately what is the total combined number of
kilometers run by the team in the race?
(A) 11
(B) 10
(C) 9
(D) 8
28. A scanner can scan 12 photos per minute. At this rate, how many
minutes would it take to scan 60 photos?
(A) 2
(B) 3
(C) 5
(D) 7
29. An employee’s net pay is equal to gross pay minus total deductions.
A certain employee’s gross pay is $1,769.23 and her deductions are
as follows: FICA, $218.99; Social Security, $107.05; Medicare,
$25.03; state tax, $68.65; municipal tax, $42.75. What is the
employee’s net pay?
(A) $1,306.76
(B) $1,306.66
(C) $1,305.76
(D) $1,305.66
30. A student takes four tests. His grades are 94, 72, 84, and 98. What is
this student’s average test grade?
(A) 92
(B) 65
(C) 87
(D) 88
IF YOU FINISH BEFORE THE TIME IS UP, YOU MAY CHECK
OVER YOUR WORK ON THIS PART ONLY.
STOP
ASVAB PRACTICE TEST A
Part 3: Word Knowledge (WK)
11
Minutes
— 35
Questions
Directions: In this section, you are tested on the meaning of words.
Each of the following questions has an underlined word. Select the
answer that most nearly means the same as the underlined word
and mark the corresponding oval on your answer sheet.
1. Impose most nearly means
(A) create
(B) force
(C) damage
(D) trade
2. Stunted most nearly means
(A) halted
(B) frightened
(C) aged
(D) overstated
3. A sturdy home can withstand nearly any disaster.
(A) huge
(B) strong
(C) cold
(D) cautious
4. He was undeterred in his quest to find her.
(A) surprised
(B) persistent
(C) careless
(D) brazen
5. Ennui most nearly means
(A) patient
(B) gloating
(C) boredom
(D) tasteful
6. Mutable most nearly means
(A) changeable
(B) silent
(C) big-hearted
(D) calm
7. The way they squandered the money was shameful.
(A) gathered
(B) stole
(C) wasted
(D) owned
8. The handwriting was nearly illegible.
(A) unreadable
(B) unethical
(C) creative
(D) dangerous
9. Infinite most nearly means
(A) costly
(B) unending
(C) babyish
(D) daily
10. Longevity most nearly means
(A) training
(B) duration
(C) girth
(D) lifestyle
11. Tourists always fall for that ruse.
(A) trick
(B) display
(C) itinerary
(D) backtalk
12. The president proclaimed it a national holiday.
(A) suggested
(B) renamed
(C) announced
(D) unmade
13. Even the most rudimentary details are crucial to understanding this
problem.
(A) basic
(B) ecstatic
(C) illogical
(D) fancy
14. Rout most nearly means
(A) careful
(B) defeat
(C) blatant
(D) open
15. His rogue attitude didn’t fit the “team” concept.
(A) aggressive
(B) sad
(C) rebellious
(D) low-brow
16. Her point of view didn’t resonate with everyone on the committee.
(A) create irritation
(B) display clarity
(C) evoke agreement
(D) generate discussion
17. Duplicating steps is far too redundant at this late stage.
(A) repetitive
(B) upsetting
(C) colorful
(D) wishy-washy
18. Far be it from me to prescribe how to raise one’s own children.
(A) predict
(B) dictate
(C) judge
(D) decide
19. Logical most nearly means
(A) cognizant
(B) easy
(C) rowdy
(D) sensible
20. Prerequisite most nearly means
(A) requirement
(B) evaluation
(C) glee
(D) good taste
21. It seems that loud people tend to gravitate toward other loud
people.
(A) be drawn
(B) be hostile
(C) be inquisitive
(D) be competitive
22. The police felt it was best to be cautious when approaching the
house.
(A) excited
(B) apathetic
(C) dodgy
(D) careful
23. Braggart most nearly means
(A) clown
(B) leader
(C) boaster
(D) deputy
24. Basing his opinions on hearsay doomed the case.
(A) rumor
(B) samples
(C) truth
(D) belief
25. Taunt most nearly means
(A) grade
(B) relate
(C) ridicule
(D) party
26. Most of our employees respond well to constructive criticism.
(A) damaging
(B) productive
(C) gentle
(D) flattering
27. Quantifiable most nearly means
(A) laughable
(B) standard
(C) countable
(D) breakable
28. The least effective way of dealing with children is yelling.
(A) tantalizing
(B) creative
(C) useful
(D) positive
29. Apathy most nearly means
(A) greatness
(B) laziness
(C) disinterest
(D) boredom
30. It le a glaring blemish on his permanent record.
(A) impact
(B) defect
(C) commendation
(D) compliment
31. It will take a consensus to get this measure passed.
(A) agreement
(B) discussion
(C) infighting
(D) reprimand
32. No coach can handle dissent from his players for long.
(A) discussion
(B) laughter
(C) laziness
(D) insubordination
33. Tempo most nearly means
(A) heartbeat
(B) safety
(C) modernity
(D) speed
34. She can take solace in the fact that it couldn’t get much worse.
(A) protection
(B) comfort
(C) glee
(D) depth
35. Many pitfalls await the inexperienced climber.
(A) joys
(B) traps
(C) ropes
(D) talents
IF YOU FINISH BEFORE THE TIME IS UP, YOU MAY CHECK
OVER YOUR WORK ON THIS PART ONLY.
STOP
ASVAB PRACTICE TEST A
Part 4: Paragraph Comprehension
(PC)
13 Minutes — 15 Questions
Directions: This section contains paragraphs followed by
incomplete statements or questions. For each question, read the
paragraph and select the answer that best completes the
statements or answers the question that follows. Mark the
corresponding oval on your answer sheet.
Questions 1 and 2 refer to the following passage.
In modern society, a form of folktale called the urban legend has emerged.
These stories persist both for their entertainment value and for the
transmission of popular values and beliefs. Urban legends are stories many
have heard; they are supposed to have really happened, but they cannot
be verified. It turns out that the people involved can never be found.
Researchers of urban legends call the elusive participant in these
supposedly “real-life” events a “FOAF”: friend of a friend.
One classic urban legend involves alligators in the sewer systems of major
metropolitan areas. According to the story, before alligators were a
protected species, people vacationing in Florida purchased baby alligators
to take home as souvenirs. A er the novelty of having a pet alligator wore
off, people would flush their souvenirs down the toilet. The baby alligators
found a perfect growing environment in city sewer systems, where to this
day they thrive on an ample supply of rats.
1. The passage suggests that the real-life participants of urban
legends
(A) can be very difficult to track down
(B) are usually known, but only barely, by the teller
(C) are friends with a large number of people
(D) are the original tellers of the stories
2. According to the passage, the successful urban legend contains all
of the following characteristics EXCEPT
(A) the capacity to entertain
(B) messages that conform to popular values
(C) qualities of a folktale
(D) a basis in reality
3. For most students of biology, Charles Darwin is considered the
father of evolution. But few realize that he was but one of many
theorists who noticed that the genetics of animals showed
progression over time. Henri Bergson, for instance, formulated a
theory that today is known more commonly as theistic evolution, or
evolution from God. However, Darwin’s ability to articulate his
theories in writing and to account for many diverse examples of
evolutionary biology means that other theories are o en seen as
little more than offshoots of the original idea of Darwinian
evolution.
According to the passage, Darwin’s theory persists because
(A) Bergson’s theory was incorrect
(B) Darwin’s theory accounted for many examples of evolution
(C) genetics is an inexact science
(D) evolution is not accepted by the mainstream
4. Local elementary schools have changed considerably over the past
50 years. Where once we had schools in every small town, now
students bus for miles to attend larger, more advanced schools.
While most parents see this as a positive step for progress and
education, some worry about their children losing touch with the
simple things around them. A few have even decided to
homeschool their children instead of sending them to nearby
towns.
The author’s tone in this passage is
(A) embittered
(B) informative
(C) biased
(D) ambivalent
Questions 5 and 6 refer to the following passage.
Most life is fundamentally dependent on photosynthetic organisms that
store radiant energy from the Sun. In almost all the world’s ecosystems and
food chains, photosynthetic organisms such as plants and algae are eaten
by other organisms, which are then consumed by still others. The existence
of organisms that are not dependent on the Sun’s light has long been
established, but until recently they were regarded as anomalies.
Over the last 20 years, however, research in deep-sea areas has revealed
the existence of entire ecosystems in which the primary producers are
chemosynthetic bacteria that are dependent on energy from within the
Earth itself. Indeed, the growing evidence suggests that these sub-sea
ecosystems model the way in which life first came about on this planet.
5. The passage suggests that most life is ultimately dependent on
which of the following?
(A) photosynthetic algae
(B) the world’s oceans
(C) bacterial microorganisms
(D) light from the Sun
6. Which of the following conclusions about photosynthetic and
chemosynthetic organisms is supported by this passage?
(A) Both perform similar functions in different food chains
(B) Both are known to support communities of higher organisms
at great ocean depths.
(C) Sunlight is the basic source of energy for both.
(D) Chemosynthetic organisms are less nourishing than
photosynthetic organisms.
7. Halley’s Comet has been known since at least 240 B.C.E. and
possibly since 1059 B.C.E. Its most famous appearance was in 1066
C.E. when it appeared right before the Battle of Hastings. It was
named a er the astronomer Edmund Halley, who calculated its
orbit. He determined that the comets seen in 1530 and 1606 were
the same object following a 76-year orbit. Unfortunately, Halley
died in 1742, never living to see his prediction come true when the
comet returned on Christmas Eve 1758.
It can be inferred from the passage that the appearance of Halley’s
Comet in 1758
(A) presaged catastrophic events in world history
(B) could not have been foreseen
(C) shocked the scientific community
(D) confirmed Halley’s calculations
8. Both alligators and crocodiles can be found in southern Florida,
particularly in the Everglades National Park. Alligators and
crocodiles look similar but there are several physical characteristics
that differentiate the two giant reptiles. The most easily observed
difference between alligators and crocodiles is the shape of the
head. The crocodile’s skull and jaws are longer and narrower than
the alligator’s. When a crocodile closes its mouth, the long teeth
remain visible, protruding outside the upper jaw. When an alligator
closes its mouth, those long teeth slip into sockets in the upper jaw
and disappear. In general, if you can still see a lot of teeth even
when the animal’s mouth is closed, you are looking at a crocodile.
According to the passage, one can distinguish a crocodile from an
alligator
(A) only when the animal’s mouth is closed
(B) by the location in Florida where the animal is found
(C) by its thick, heavily armored skin
(D) by the narrower snout found on a crocodile
9. A talent agent analyzed her company’s records in an attempt to
determine why it was placing so few actors in roles. She attributed
the company’s poor performance to the fact that o en the actors
sent to an audition were completely inappropriate for the role.
It can be inferred from the passage that the agent believes that
(A) certain actors are inappropriate for certain roles
(B) the actors her company represents are not very good
(C) it is difficult to predict how appropriate an actor will be for a
role
(D) her company does not send enough actors to audition for
major roles
10. One of the most commonly used of all poetic meters is iambic
pentameter. Pentameter refers to the number of feet, or groupings
of syllables. The prefix penta–means five, so a poem written in
pentameter has five feet per line. In iambic pentameter, the type of
foot used is an iamb. An iamb is a word or words with two syllables
with the stress on the second syllable. William Shakespeare is
perhaps the most famous writer of iambic pentameter.
Shakespeare composed hundreds of poems and plays in this meter
and popularized it for the masses.
According to the passage, a foot is
(A) a grouping of syllables
(B) similar to a meter
(C) an innovation credited to William Shakespeare
(D) a type of poem
11. It is o en said that American involvement in World War I would not
have begun in earnest were it not for the German sinking of the
passenger ship the Lusitania on February 18, 1915. Preferring prior
to then to stay neutral in the war, America was until that time
offering only financial and tactical support for Britain and France
against Germany and Austria-Hungary. The sinking of the huge
passenger ship, however, altered public opinion about U.S.
involvement and subsequently led to military escalation, truly
making the war a matter for the whole world.
The main idea of the passage is that
(A) the Germans sank the Lusitania because of America’s financial
and tactical support for Britain and France
(B) Austria-Hungary and Germany were allies in World War I
(C) American involvement in World War I was minimal
(D) the sinking of the Lusitania prompted increased American
involvement in World War I
12. When a movie criticized by most film critics is a popular success, it
is o en seen as a sign of poor taste on the part of general
audiences. But there is little diversity among film critics, and the
critics’ preferences are o en a product of their backgrounds and
class prejudices. Thus, their opinions are no more likely to be an
unerring guide to quality than those of the average moviegoer.
The passage above best supports which of the following
conclusions?
(A) Judgments of film quality by professional film critics are
usually wrong.
(B) Judgments of quality applied to movies are meaningless.
(C) Film critics usually consider popular movies to be of poor
quality.
(D) When critics and general audiences disagree about a movie’s
quality, the critics’ opinion is not necessarily more valid.
13. The tomato originated in the New World. It was first domesticated
around 700 C.E. by the Aztec and Incan civilizations. In the sixteenth
century, European explorers were so appreciative of the tomato
that they introduced it to the rest of Europe. Although the French,
Spanish, and Italians quickly began to adapt their recipes to use
tomatoes, the English considered tomatoes poisonous. This myth
traveled to the colonies, where settlers in America continued to
avoid the supposedly deadly tomato. It wasn’t until the middle
1800s that the tomato began to gain acceptance in the U.S.
According to the passage, Americans did not start using the tomato
until the mid-nineteenth century because
(A) it was unavailable in the New World
(B) they lacked recipes for using it
(C) they believed it to be poisonous
(D) it was viewed as a Mediterranean food
14. Daria has been picking up many extra shi s at the local restaurant.
Her school work has also been increasing at an alarming rate. The
past few weeks have le Daria feeling very drowsy. She looks
forward to heading to bed each night and getting as much sleep as
possible.
What does the word “drowsy” mean in context?
(A) drunk
(B) tired
(C) happy
(D) satisfied
15. The sun was relentless as I started my hike through the woods.
Sitting under the large branches of the trees was the only way I was
able to escape the oppressive heat. Without the leafy canopy
sheltering me throughout my journey, I would have had to cut my
hike short.
The author implies which of the following about the trees in the
forest?
(A) They provide adequate shade.
(B) They do not provide adequate shade.
(C) They impair her ability to enjoy the sunshine.
(D) They provide a home to many animals.
IF YOU FINISH BEFORE THE TIME IS UP, YOU MAY CHECK
OVER YOUR WORK ON THIS PART ONLY.
STOP
ASVAB PRACTICE TEST A
Part 5: Mathematics Knowledge (MK)
24
Minutes
— 25
Questions
Directions: In this section, you will be tested on your knowledge of
basic mathematics. For each question, select the best answer and
mark the corresponding oval on your answer sheet.
1. For all x, (3x + 4)(4x − 3) =
(A) 7x − 12
(B) 12x2 − 12
(C) 12x2 − 25x − 12
(D) 12x2 + 7x − 12
2. If a tree grew 5 feet in n years, what was the average rate at which
the tree grew, in inches per year?
(A)
(B)
(C)
(D)
3.
In the figure above, if the perimeter of rectangle ABCD is 56, and the
length of AD is 16, what is the area of ABCD?
(A) 40
(B) 64
(C) 160
(D) 192
4. A square is a rectangle with four
sides.
(A) equal
(B) parallel
(C) unequal
(D) curvilinear
5. If a < b and b < c, which of the following must be true?
(A) b + c < 2a
(B) a + b < c
(C) a − b < b − c
(D) a + b < 2c
6. In the figure above, x = 2z and y = 3z. What is the value of z?
(A) 24
(B) 30
(C) 36
(D) 54
7. If the minute hand of a properly functioning clock has just moved
45 degrees, how many minutes passed while it did so?
(A) 6
(B) 7.5
(C) 12.5
(D) 27
8. What is the area of the figure below?
(A) 4
(B) 6
(C) 12
(D) 24
9. In the figure below, if line p is parallel to line q, what is the value of
y?
(A) 65
(B) 115
(C) 125
(D) 130
10. 15% of 15% of 200 is
(A) 4.5
(B) 6
(C) 12.5
(D) 45
11. What is the average (arithmetic mean) of
and
?
(A)
(B)
(C)
(D)
12. If an angle measures y°, what will its supplement measure in terms
of y?
(A) (90 − y)°
(B) (90 + y)°
(C) (180 − y)°
(D) (180 + y)°
13. Diane painted
of her room with 2
cans of paint. How many more cans of paint will she need to
finish painting her room?
(A) 2
(B) 5
(C) 7
(D) 10
14. If 13 + a = 25 + b, then b − a =
(A) 12
(B) 8
(C) −8
(D) −12
15. For all x, 3x2 × 5x3 =
(A) 8x5
(B) 8x6
(C) 15x5
(D) 15x6
16. If the sides of a square increase in length by 10%, the area of the
square increases by
(A) 10%
(B) 15%
(C) 20%
(D) 21%
17. If
, then
=
(A) 7.5
(B) 10
(C) 22.5
(D) 30
18. Which of the following is a factor of 6x2 − 13x + 6?
(A) 2x + 2
(B) 2x + 3
(C) 3x − 2
(D) 3x − 3
19. If the product of 3 and x is equal to 2 less than y, which of the
following must be true?
(A)
(B) 3x − y − 2 = 0
(C) 3x + y − 2 = 0
(D) 3x − y + 2 = 0
20. If x > 1 and
then
=
(A)
(B)
(C) x − 1
(D)
21.
If the solid above is half of a cube, then the volume of the solid is
(A) 16
(B) 16
(C) 32
(D) 32
22. When 7.6 is divided by 0.019, the quotient is
(A) 4,000
(B) 400
(C) 40
(D) 4
23. What is the area of a circle with a circumference of 8?
(A)
(B)
(C) 4π
(D) 16π
24. 36% of 18 is 18% of what number?
(A) 9
(B) 36
(C) 72
(D) 200
25.
is between which two numbers?
(A) 100 and 200
(B) 200 and 300
(C) 300 and 400
(D) 400 and 500
IF YOU FINISH BEFORE THE TIME IS UP, YOU MAY CHECK
OVER YOUR WORK ON THIS PART ONLY.
STOP
ASVAB PRACTICE TEST A
Part 6: Electronics Information (EI)
9
Minutes
— 20
Questions
Directions: In this section, you will be tested on your knowledge of
electronics basics. For each question, select the best answer and
mark the corresponding oval on your answer sheet.
1. Resistance is measured in
(A) amperes
(B) ohms
(C) V
(D) W
2. Protons have a
charge, and neutrons are
charged.
(A) positive, negatively
(B) positive, neutrally
(C) negative, positively
(D) neutral, negatively
3. What is the term for a current flowing in a conductor which changes
direction (moves back and forth) many times in a second?
(A) alternating current
(B) direct current
(C) electromotive force
(D) variable current
4. What type of circuit does this symbol represent?
(A) parallel circuit
(B) series circuit
(C) series-parallel circuit
(D) short circuit
5. In the formula for Ohm’s Law, V = I × R, the I represents
(A) voltage
(B) current
(C) resistance
(D) impedance
6. The P-type material in a diode is also known as the
(A) electrode
(B) cathode
(C) base
(D) anode
7. Introducing impurities into the crystal structure of silicon is also
known as
(A) tinning
(B) enhancing
(C) processing
(D) doping
8. Which of the following causes the least resistance to a high
frequency alternating current?
(A) capacitor
(B) fixed resistor
(C) variable resistor
(D) inductor
9. A circuit contains four resistors of 2 Ω, 4 Ω, 6 Ω, and 8 Ω in series.
What is their effective resistance?
(A) 2 Ω
(B) 5 Ω
(C) 8 Ω
(D) 20 Ω
10. All of the following statements about transistors are true EXCEPT
(A) N-type material has free electrons
(B) NPN transistors require a positive voltage at the base to turn
them on
(C) the arrow in the transistor symbol is always placed on the
collector
(D) P-type material conducts current through the movement of
holes
11. This is the symbol for which type of meter?
(A) voltmeter
(B) ammeter
(C) ohmmeter
(D) galvanometer
12. Which of the following is NOT an essential component of an
electrical circuit?
(A) voltage source
(B) watt
(C) load
(D) conductor
13. What type of switch would be utilized by a doorbell?
(A)
(B)
(C)
(D)
14. Which of the following is the symbol for an AC voltage source?
(A)
(B)
(C)
(D)
15. Capacitors are also known as
(A) capacitances
(B) dielectrics
(C) condensers
(D) inductors
16. A material that will not conduct electricity is known as
(A) a conductor
(B) a semiconductor
(C) an insulator
(D) a voltage source
17. Which of the following materials is NOT a conductor?
(A) rubber
(B) silver
(C) copper
(D) aluminum
18. A circuit with four 6-ohm resistors wired in series has 12 volts
applied to it. What current flows through this circuit?
(A) 5 mA
(B) 50 mA
(C) 500 mA
(D) 5 A
19. An element that is widely recognized as a semiconductor is
(A) silicon
(B) aluminum
(C) helium
(D) wood
20. This is the symbol for which type of meter?
(A) voltmeter
(B) ammeter
(C) ohmmeter
(D) galvanometer
IF YOU FINISH BEFORE THE TIME IS UP, YOU MAY CHECK
OVER YOUR WORK ON THIS PART ONLY.
STOP
ASVAB PRACTICE TEST A
Part 7: Auto and Shop Information
(AS)
11
Minutes
— 25
Questions
Directions: In this section, you will be tested on your knowledge of
automotive and shop basics. For each question, select the best
answer and mark the corresponding oval on your answer sheet.
1. Wood can be shaped using all of the following tools EXCEPT
(A) jack plane
(B) wood chisel
(C) flat rasp
(D) miter box
2. Ride quality is the job of the vehicle’s
system.
(A) steering
(B) suspension
(C) charging
(D) brake
3. The cut in the wood le behind by a saw is known as the
(A) gap
(B) line
(C) trace
(D) kerf
4. A four-wheel drive vehicle uses a
the front and rear drive axles.
(A) transmission
(B) drive sha
(C) torque converter
(D) transfer case
to distribute power to
5. What type of cut is this saw made for?
(A) a cut with the grain of the wood
(B) a cut across the grain of the wood
(C) a cut made in plywood only
(D) a cut made in steel only
6. This image depicts what stroke in the four-stroke cycle?
(A) intake stroke
(B) power stroke
(C) compression stroke
(D) exhaust stroke
7. Thread pitch of a fractional measurement fastener is determined by
(A) counting the number of threads per inch
(B) measuring the distance in millimeters between threads
(C) measuring the distance in inches between threads
(D) counting the number of threads per millimeter
8. Which would be best to use to loosen tight fasteners?
(A)
(B)
only this tool:
only this tool:
(C) only this tool:
(D) the tools shown in both (B) and (C)
9. All of the following are parts of the vehicle’s steering system
EXCEPT
(A) coil spring
(B) steering knuckle
(C) tie rod end
(D) idler arm
10. Which engine component is responsible for the opening and
closing of the engine’s intake and exhaust valves?
(A) 1
(B) 2
(C) 3
(D) 4
11. On a fuel-injected engine, the fuel pump is normally located
(A) on the engine
(B) on the vehicle frame
(C) near the rear bumper
(D) in the fuel tank
12. UNC fasteners have
threads per inch when compared
to UNF fasteners of the same diameter.
(A) the same number of
(B) fewer
(C) twice as many
(D) thrice as many
13. In power brake systems, braking pressures are increased using
(A) only the engine intake manifold vacuum
(B) only the fluid pressure from the power steering system
(C) both the engine intake manifold vacuum and fluid pressure
from the power steering system
(D) neither the engine intake manifold vacuum nor the fluid
pressure from the power steering system
14. All of the following are parts of the ignition primary system EXCEPT
the
(A) battery
(B) ignition switch
(C) reluctor and pickup
(D) rotor
15. “Stoichiometric” is a term that describes
(A) the ideal air-fuel mixture in a gasoline engine
(B) the voltage required to generate a spark
(C) the engine’s breathing efficiency
(D) theoretical horsepower
16. An oil’s resistance to flow is known as its
(A) quality rating
(B) pumpability
(C) lubricity
(D) viscosity
17. All cars are currently being built with
systems.
electrical
(A) only direct current
(B) only alternating current
(C) both direct and alternating current
(D) neither direct nor alternating current
18. When arc-welding, the ground clamp should be connected to the
(A) floor
(B) welding rod
(C) electrical outlet
(D) work
19. What cylinder design is referred to as a “boxer” engine?
(A) inline only
(B) flat only
(C) horizontally opposed only
(D) both flat and horizontally opposed
20. What are these tools used for?
(A) securing a rivet in place where a tight rivet is important
(B) striking an object where it is important that the hammer itself
not come in direct contact with the work
(C) driving small fasteners and making layout marks in metalwork
(D) guiding a saw when making a cutting across the grain
21. In a V-type engine with two cylinder heads, which of these designs
would have two camsha s, with one installed above each cylinder
head?
(A) single overhead cam or SOHC
(B) double overhead cam or DOHC
(C) triple overhead cam or TOHC
(D) overhead value or OHV
22. Air entering an engine’s combustion chamber must pass through
each of the following EXCEPT
(A) the air filter
(B) the intake manifold
(C) the intake port in the cylinder head
(D) the catalytic converter
23. Which tool would be best suited for loosening a very tight nut?
(A) open-end wrench
(B) 12-point socket and breaker bar
(C) 6-point socket and ratchet
(D) 6-point socket and breaker bar
24. What type of retaining ring is depicted here?
(A) internal prong-type
(B) internal hole-type
(C) external “E”-type
(D) external hole-type
25. As a car’s battery discharges its energy, which of the following takes
place in the battery’s lead plates?
(A) They release water.
(B) They are converted to lead sulfate.
(C) They discharge impurities.
(D) They are converted to electrolytes.
IF YOU FINISH BEFORE THE TIME IS UP, YOU MAY CHECK
OVER YOUR WORK ON THIS PART ONLY.
STOP
ASVAB PRACTICE TEST A
Part 8: Mechanical Comprehension
(MC)
19
Minutes
— 25
Questions
Directions: In this section, you will be tested on your knowledge of
mechanics and basic physics. Select the best answer for each
question and mark the corresponding oval on your answer sheet.
1. A car rolls down a hill. It travels progressively faster because
(A) its potential energy is being converted into kinetic energy
(B) its kinetic energy is being converted to potential energy
(C) its energy is maximized
(D) its energy is minimized
2. When a ball is thrown into the air, it has its maximum potential
energy when
(A) it leaves the hand of the person throwing it
(B) it enters the hand of the person catching it
(C) its velocity is zero
(D) its velocity is greatest
3. Objects that require more force to get them moving have greater
(A) momentum
(B) inertia
(C) torque
(D) pressure
4. Isaac Newton discovered that every particle in the universe is
attracted to every other particle. This law is called Newton’s
(A) first law of motion
(B) third law of motion
(C) law of universal gravitation
(D) second law of motion
5. A 30N force is applied to 5 kg box. Assuming no friction, what is the
acceleration gained by the box?
(A) 0.15 m/s2
(B) 0.6 m/s2
(C) 1.5 m/s2
(D) 6 m/s2
6. Compared to li ing a heavy box directly from ground level up to the
top of a ramp, pushing the box up the ramp (neglecting friction) is
doing:
(A) less work
(B) more work
(C) the same amount of work
(D) no work
7. All of the following statements about work are true EXCEPT
(A) force is a factor of work
(B) it is possible to get more work out of a machine than what is
put in
(C) to do work, an object must be moved
(D) work can be measured in foot-pounds
8. A chisel is illustrated below. A chisel is an example of a(n)
(A) wedge
(B) first-class lever
(C) inclined plane
(D) wheel and axle
9. The difference between a wedge and an inclined plane is
(A) a wedge has a steeper slope than an inclined plane
(B) a wedge is made to move, whereas an inclined plane stays
stationary
(C) a wedge stays stationary, whereas an inclined plane is made to
move
(D) a wedge has less friction
10. Which post holds up the greater part of the load?
(A) post A
(B) post B
(C) both hold up the load equally
(D) answer cannot be determined based on information provided
11. Work and kinetic energy are both measured in
(A) kilograms
(B) meters per second
(C) joules
(D) newtons
12. The design of a screwdriver is based on which of the following
simple machines?
(A) inclined plane
(B) wheel and axle
(C) first-class lever
(D) pulley
13. An increase in force accomplished through mechanical advantage
is always accompanied by
in distance moved.
(A) an increase
(B) a decrease
(C) no change
(D) an increase at times and a decrease at other times
14. The design of a prybar, as illustrated, is based on which of the
following simple machines?
(A) first-class lever
(B) second-class lever
(C) third-class lever
(D) inclined plane
15. One horsepower is equal to how many watts?
(A) 550
(B) 746
(C) 10,000
(D) 100
16. In order to increase force with a first-class lever, the fulcrum should
be
(A) moved toward where the effort is applied
(B) kept in the same position
(C) moved toward where the object is moved
(D) removed altogether
17. Which of the following statements is correct?
(A) The work put out by a simple machine can sometimes exceed
the work put in.
(B) The work put out by a simple machine always exceeds the
work put in.
(C) The work put out by a simple machine can never exceed the
work put in.
(D) The work put out by a simple machine is equal to and opposite
of the work put in.
18. If a small gear drives a large gear, a
(A) mechanical advantage
(B) block and tackle
(C) torque multiplication
(D) reduction in rotational speed
takes place.
19. A block and tackle, as shown below, utilizes
(A) a single pulley
(B) multiple pulleys
(C) only moveable pulleys
(D) only fixed pulleys
20. The force required by a person pulling on a rope using a single
pulley to li an object is equal to
(A) the weight of the object
(B) twice the weight of the object
(C) one half of the weight of the object
(D) the weight of the object divided by the diameter of the pulley
21. The design of a doorknob is based on which of the following simple
machines?
(A) inclined plane
(B) wheel and axle
(C) first-class lever
(D) pulley
22. An astronaut’s mass is 30 kg on Earth. What is his mass on the
Moon?
(A) the same
(B) lower
(C) higher
(D) cannot be determined
23. In a gear train, torque and speed can be described as
(A) exactly the same
(B) directly proportional
(C) inversely proportional
(D) sometimes proportional
24. An object’s potential energy can be calculated using the formula
(A) PE =
m × v2
(B) PE = m × v
(C) PE = m × g × ℎ
(D) PE = m × a
25. A child applies a 10 N force to a large box. The box however, does
not move. How much work has the child done?
(A) 0 J
(B) 5 J
(C) 10 J
(D) 100 J
IF YOU FINISH BEFORE THE TIME IS UP, YOU MAY CHECK
OVER YOUR WORK ON THIS PART ONLY.
STOP
ASVAB PRACTICE TEST A
Part 9: Assembling Objects (AO)
15
Minutes
— 25
Questions
Directions: In this section, you will be tested on your ability to
determine how an object will look when its parts are put together.
For each question, select the best answer and mark the
corresponding oval on your answer sheet.
1.
(A)
(B)
(C)
(D)
2.
(A)
(B)
(C)
(D)
3.
(A)
(B)
(C)
(D)
4.
(A)
(B)
(C)
(D)
5.
(A)
(B)
(C)
(D)
6.
(A)
(B)
(C)
(D)
7.
(A)
(B)
(C)
(D)
8.
(A)
(B)
(C)
(D)
9.
(A)
(B)
(C)
(D)
10.
(A)
(B)
(C)
(D)
11.
(A)
(B)
(C)
(D)
12.
(A)
(B)
(C)
(D)
13.
(A)
(B)
(C)
(D)
14.
(A)
(B)
(C)
(D)
15.
(A)
(B)
(C)
(D)
16.
(A)
(B)
(C)
(D)
17.
(A)
(B)
(C)
(D)
18.
(A)
(B)
(C)
(D)
19.
(A)
(B)
(C)
(D)
20.
(A)
(B)
(C)
(D)
21.
(A)
(B)
(C)
(D)
22.
(A)
(B)
(C)
(D)
23.
(A)
(B)
(C)
(D)
24.
(A)
(B)
(C)
(D)
25.
(A)
(B)
(C)
(D)
IF YOU FINISH BEFORE THE TIME IS UP, YOU MAY CHECK
OVER YOUR WORK ON THIS PART ONLY.
STOP
CONGRATULATIONS!
You have completed ASVAB Practice Test A. Check your work using
the explanations that begin on the next page.
Answers and Explanations
PART 1: GENERAL SCIENCE (GS)
1. A
The levels of classification, from largest to smallest, are: kingdom,
phylum, class, order, family, genus, species. Thus, a genus is a group
that contains related species.
2. B
Electrons orbit the nucleus of an atom.
3. D
As a human inhales, the incoming air first passes through the nasal
cavity, where it is both warmed and filtered.
4. D
A tertiary consumer is an animal that consumes secondary consumers,
or other carnivores. Coyotes are the tertiary consumer in this food chain.
They feed on foxes, which in turn feed on rabbits. Dandelions represent
the producers in the food chain.
5. B
The process by which a solid becomes a gas is sublimation. Boiling, (A),
is the process by which a liquid becomes gas. Melting, (C), is the process
by which a solid becomes a liquid. Diffusion, (D), describes the process
by which a gas or liquid intermingles with another.
6. C
The gravitational force the Moon exerts on the Earth is the same as the
gravitational force the Earth exerts on the Moon. According to Newton’s
third law, for every force exerted on object A by object B, object B
experiences an equal and opposite force from object A. Thus, when the
Earth exerts its gravitational force on an object, such as the Moon, the
Moon exerts an equal and opposite force on the Earth.
7. B
Fungi are decomposers (also known as saprophytes), returning the
organic material from dead matter such as leaves, trees, and animal
remains back into the environment. Producers, (A), make their own food.
Consumers, (C), must eat other organisms in order to gain energy.
Mutualism, (D), is a type of symbiosis whereby both organisms benefit.
8. D
The freezing point of water on the Kelvin scale occurs at 273 K. Kelvin
and Celsius share a similar scale (i.e., a change of one Kelvin is the same
as a change of one degree Celsius). However, they differ by 273 units. To
convert Celsius to Kelvin, add 273. To convert Kelvin to Celsius, subtract
273. Since water freezes at 0 degrees Celsius, this is equivalent to 0 + 273
= 273 K.
9. A
Tough elastic tissues found in the joints that connect bones to bones are
called ligaments. Tendons are connective tissues that unite a muscle
with some other part, such as a bone. Cartilage is a somewhat elastic
tissue (unlike bone). In adults it is found in joints (where it helps reduce
friction between bones), in respiratory passages, and in the external ear.
Although cartilage appears in joints where bones meet, its role is not to
hold them together, but to keep them apart, acting as a buffer to
prevent rubbing and wear. Finally, muscles are body tissue consisting of
long cells that contract when stimulated to produce motion.
10. B
Stress, a poor diet, cigarette smoking, and heredity are all factors that
are linked to high blood pressure.
11. A
Cirrus clouds are the thin, wispy clouds that occur very high in the
atmosphere, at elevations of 20,000 feet or more. Stratus and cumulus
clouds are both low-forming. Stratocumulus clouds contain clumps of
clouds and are not thin or wispy.
12. C
Fossils are most likely to be found in sedimentary rock such as shale,
which is rock formed by the sedimentation of clay, mud, or silt.
Sedimentary rock is composed of minerals and other matter, such as
animal remains.
13. B
Animals that consume only plants are called herbivores. Carnivores, (C),
consume meat. Omnivores, (D), consume both meat and plants.
Saprophytes, (A), gain their nutrients through dead organisms.
14. D
The Sun is a fairly young star and therefore has lower temperature and
luminosity, resulting in its yellow color. The Sun is also fairly small as
stars go and falls under the “dwarf” category.
15. D
A population is a group of organisms of the same species living in the
same region. Biomes, ecosystems, and communities all encompass
more than one type of species.
16. D
The four planets beyond Mars—Jupiter, Saturn, Uranus, and Neptune,
are referred to as the outer planets. Earth is one of the four planets
closest to the Sun and is thus considered an inner planet.
17. B
A boulder that begins to roll down a hill is an example of an energy
conversion from potential energy to kinetic energy. The boulder has
maximum potential energy at the top of the hill, and this energy is
converted into kinetic energy as the boulder rolls down the hill and
picks up speed. At the foot of the hill, all potential energy has been
converted into kinetic energy.
18. D
The lowest layer of the Earth’s atmosphere is called the troposphere.
This layer extends from the surface to the bottom of the stratosphere.
Most weather changes occur here and the temperature generally
decreases rapidly with altitude.
19. B
According to the law of conservation of energy, energy can neither be
created nor destroyed. Instead, it changes from one form to another.
20. C
As an ambulance approaches, the sound waves from its siren are
compressed toward the observer. The intervals between waves
diminish, which translates into an increase in frequency or pitch. As the
ambulance recedes, the sound waves are stretched relative to the observer, causing the siren’s pitch to decrease. By the change in pitch of
the siren, one can determine if the ambulance is coming nearer or
speeding away. This perceived change in pitch is known as the Doppler
effect.
21. D
A concave lens—one that is thicker on the edges than it is in the middle
—is also known as a diverging lens because it diverges the light waves
that pass through it.
22. D
A molecule is the smallest particle of an element or compound that can
exist in a free state and still retain the characteristics of the element or
compound. In elements whose atoms form covalent bonds, the
molecules consist of two or more similar atoms (e.g., N2). (Note that
atoms of some elements form metallic bonds, and these groups of
atoms are not molecules; for example, pure copper (Cu) is made up of
atoms that do not form molecules.) The molecules of covalent
compounds consist of two or more different atoms (e.g., H2O). Protons
and quarks are subatomic particles; atoms are the building blocks of
molecules.
23. C
The orbit of the Moon around the Earth, which exerts a gravitational pull
on the ocean’s waters, is the phenomenon most responsible for oceanic
tides.
24. B
The elements in a column on the Periodic Table are referred to as a
group; each member of a group has the same number of electrons in its
outer shell. Each row on the Periodic Table is referred to as a period.
25. A
When molecules undergo a chemical change, the process is called a
chemical reaction. The molecules that enter the reaction are called
reactants and the molecules that result from the reaction are called
products.
Answers and Explanations
PART 2: ARITHMETIC REASONING (AR)
1. D
The ratios of apples to pears and pears to oranges for a given cost are
provided. What’s needed to solve this problem, however, is the ratio of
apples to oranges. To merge these into one ratio relating all three fruits,
you need to express both ratios using the same number of pears. In one
ratio it’s 4, and in the other it’s 3. Since the least common multiple of 3
and 4 is 12, you can multiply both individual ratios so that the number of
pears comes to equal 12: apples:pears = 3:4 = 9:12 (multiply both sides of
the ratio by 3) pears:oranges = 3:2 = 12:8 (multiply both sides of the ratio
by 4) Now you can combine the ratios:
apples : pears : oranges
9:12:8
Now you can also state the ratio of apples to oranges: apples:oranges = 9:8
Given a value for the number of oranges as 72, you can now set up a
proportion:
Cross-multiply and solve for x:
= . Cross-multiply, getting 8x = (9)(72). Divide both sides by 8 to
get
. To make the arithmetic easier, divide 72 by 8 first, which
equals 9, then multiply this answer by 9, getting 9 × 9 = 81.
2. C
If 48 of 60 seats are occupied, then 12 of 60 seats are unoccupied (since 60
− 48 = 12). What percent of the seats are unoccupied?
, choice (C).
3. B
Break this question down into pieces. Before midnight, Effin gets paid
$1,000 an hour. If she starts singing at 8:30 p.m., then she sings for
hours before midnight. Her earnings for that time are
× $1,000 =
$3,500. A er midnight, her rate increases 50%, so her hourly rate a er
becomes $1,000 + $1,000(50%) = $1,000 + $500 = $1,500. She works one
hour a er midnight, earning $1,500. Add the amount she earns before
midnight and the amount she earns a er midnight, so her total pay is
$3,500 + $1,500 = $5,000.
4. B
The probability of an event occurring is a fraction: the number of possible
outcomes in which the event can occur divided by the total number of
possible outcomes. Fran is going to pick one shirt and the question asks
for the probability that it will not be orange. In other words, you need to
find the probability of picking a black or blue shirt. There are 4 black shirts
and 5 blue shirts, so altogether there are 9 possible successful outcomes.
The total number of shirts to choose from, including the orange shirts, is
12, so there are 12 possible outcomes. The probability of Fran picking a
non-orange shirt is
. Since
is not available in the answer choices,
reduce the fraction by dividing the top and bottom by 3 to get
.
5. B
Newark is two hours later than Denver, so if the time in Denver when
Harry arrives is 2:30 p.m., then the time in Newark when he arrives is 4:30
p.m. The flight takes 5 hours, so the time he began in Newark is 5 hours
earlier than 4:30 p.m., or 11:30 a.m.
6. B
How many times does 24 go into 198? 198 ÷ 24 = 8 with a remainder of 6,
so Doris will have 6 pieces of chocolate le over.
7. C
If 75% of x is 150, then 0.75(x) = 150 or
(x) = 150. Multiply both sides by
and x = 200. You could also backsolve. Only choice (C), 200, works. If x =
200, then 0.75(x) = 150 since 0.75(200) = 150.
8. A
The formula for finding the average is:
Don’t just average the old average and the last test score—that would give
the last score as much weight as all the other scores combined. The best
way to deal with changing averages is to use the sums. Use the old
average to figure out the total of the first 6 scores: Sum of first 6 scores =
(83)(6) = 498
Then add the 7th score and divide:
9. B
If the charge for one pound is $25.00, then the charge for
would be
of a pound
× 25.00 = $20.00 plus 8% sales tax. 8% of $20.00 = 0.08($20.00)
= $1.60. $20.00 + $1.60 = $21.60.
10. D
To answer this question, determine how many times
goes into 60. It will
be more than 60, so right away you can eliminate (A).
. This is easier to multiply if you cancel first. 3 goes
into 60 twenty times, so replace the 3 with a 1, and replace the 60 with a
20 to get
.
11. B
Set up equations based on the information given in the problem. The
question asks for the amount of money Robert has.
Ed has 100 more dollars than Robert:
E = R + 100.
Ed then spends 20 dollars and has five times as much money as Robert: E
– 20 = 5R.
Solve a question like this using algebra if it’s a strong area for you.
Substitute R + 100 for E and solve: R + 100 – 20 = 5R
R + 80 = 5R
80 = 4R
R = $20
You could also backsolve, starting with choice (B) or (C) for Robert’s
money. If you started with (C) 24, you would plug 24 into both equations
and see if you got the same value for E.
In the first equation:
E = R + 100
E = 24 + 100
E = 124
In the second equation:
E – 20 = 5R
E – 20 = 5(24)
E – 20 = 120
E = 140
The numbers don’t match, so eliminate (C) and try (B) 20.
In the first equation:
E = R + 100
E = 20 + 100
E = 120
In the second equation:
E – 20 = 5R
E – 20 = 5(20)
E – 20 = 120
E = 120
The value for E is the same in both equations, which tells you that 20 is the
correct answer.
12. D
This question is actually a remainder question in disguise. If 587 people
are to be divided among buses that each seat 48 people, divide 587 by 48
to see how many buses would be filled completely. The remainder is the
number of people in the unfilled bus. 587 ÷ 48 = 12 with a remainder of 11.
13. C
Riley brought 100 cookies, and 25 are le over. That means that Riley and
her classmates ate 75 cookies.
14. C
This is a proportion question:
Cross-multiply to solve:
15. D
Percent times whole equals part: Percent × 25 = 16
16. A
First find how long the trip takes him at each of the two different rates,
using the formula
He travels the first 10 km at 30 km per hour, so he takes
hour = 20
minutes for this portion of the journey. He travels the remaining 30 km at
15 km per hour, so he takes
The whole journey takes him
hours for this portion of the journey.
hours = 2 hours 20 minutes.
Now calculate the amount of time it would take to make the same trip at a
constant rate of 20 km per hour. If he traveled the whole 40 km at 20 km
per hour, it would take
=2 hours. Now 3 hours is more than 2 hours
by
hour, or 20 minutes.
17. B
Since 3 out of 24 students are in student organizations, the remaining 24 –
3 = 21 students are not in student organizations. Therefore, the ratio of
students in organizations to students not in organizations is:
= .
18. A
By midseason, team A had won 60 and team B had won 49 games. Over
the remaining 80 games, team A won 40 and lost 40. That means that
team A wound up with 60 + 40 = 100 wins. To win 100 games, team B
would have to win 100 – 49 = 51 games over the remainder of the season.
19. C
A vendor bought 10 crates for a total cost of $80. He wants to make a total
profit of 25% over the total cost. So the total sale would have to equal $80
+ (0.25)($80) = $80 + $20 = $100. He lost 2 crates, so he would need to sell
the remaining 10 – 2 = 8 crates for $100 to make the required profit.
= $12.50 per crate.
20. D
Set up a proportion on questions that give rates:
Before you cross-multiply, reduce the first fraction as much as possible to
make the calculations easier. Divide the numerator and denominator by
10:
Cross-multiply:
15x = 120
Divide both sides by 15:
x=8
21. C
To figure out whether the product is positive or negative, count the
number of negatives given. If there are an odd number of negatives, the
product is negative. That eliminates (A) and (B). Multiplying the two
numbers gives: 15 × (-5) = -75.
22. B
The ratio of baseball cards to baseball figurines is
You are given the
number of cards, so you can set up a proportion:
Cross-multiply to get 5x = 175 and divide both sides by 5 so x = 35.
23. C
Set up equations to represent the relationships given in the problem: 2ℎ +
1s = $3.25
3ℎ + 1s = $4.50
The difference between the two totals is the price of a single hot dog.
Thus, a single hot dog costs: $4.50 − $3.25 = $1.25. Plug the price of a
single hot dog into the first equation to get the price of a soda:
The question asks for the cost of two sodas: 2 × $0.75 = $1.50. Always
double-check to be sure you are solving for the value the question asks
for. In this case, choice (A) is a trap answer because it is the price of one
soda.
24. A
When you are given two rates, you cannot simply take the average of the
two. Thus, answer choice (B) 50 is a trap answer here. Because it takes
more time to travel at a slower speed, the average for the entire trip will
be closer to the slower speed. To solve this problem, pick a number for
the distance of the entire trip. Since 40 and 60 are the rates, use the least
common multiple, 120, for the number of miles. First, find the time spent
traveling at each speed: 120 miles at 40 mph = 3 hours
120 miles at 60 mph = 2 hours
Total distance = 240 miles. Total time = 5 hours.
The average for the entire trip will be the total distance divided by the
total time.
25. B
Call the number of teachers n. Then the number of students is 10n. The
total number of teachers and students is n + 10n = 11n.
Since you can’t have a fraction of a person, n must be an integer, which
means the total number of teachers and students must be a multiple of
11. Scan the answer choices and locate (B), 11 × 11, as the correct answer.
None of the other answer choices are multiples of 11.
26. C
Use Backsolving for this one, beginning with choice (C). If the smaller
number is 21 (and the larger number is 35), does the math from the
question work?
The average of 21 and
The positive difference between 21 and 35 is 14. Twice the positive
difference would be 2 × 14 = 28.
Thus, 21 is the smaller number and the correct answer.
You can also solve this question algebraically. Set the smaller number
equal to y. Then, the average of the two numbers is:
. Twice the
positive difference of the two numbers is: 2(35 – y). The average is equal to
twice the positive difference, so
= 2(35 – y). Solve:
27. C
If a question uses the word “approximately” you can approximate the
answer. If each of seven runners is running a little less than 1.3 kilometers,
the total distance run would be a little less than 7 × 1.3 = 9.1, which is
approximately 9 kilometers.
28. C
Set up a proportion:
Now cross-multiply and solve: 12x = 60, so
.
29. A
This is a pure arithmetic computation question. First, add up all of the
deductions: 218.99 + 107.05 + 25.03 + 68.65 + 42.75 = 462.47
Now subtract total deductions from gross pay:
1,769.23 – 462.47 = 1,306.76.
30. C
This is a standard average problem. Take the sum of all the terms and
divide by the number of terms. 94 + 72 + 84 + 98 = 348. 348 ÷ 4 = 87. If
dividing 348 by 4 was time consuming for you, you could have used
Backsolving. Once you found the sum was 348, you could multiply the
answer choices by 4, starting with (B) or (C), to see which answer choice
gives 348. 87 × 4 = 348.
Answers
and Explanations
PART 3: WORD KNOWLEDGE (WK)
1. B
Impose as a verb means to “establish by authority.” Of the answer
choices given, only one implies one person dictating to another. To force
as a verb can be construed as “to establish by authority.” Thus, answer
choice (B) is correct. Remembered real-life context might be helpful. If
you have ever heard someone described as “an imposing figure,” you
may remember that person as an authoritative or forceful individual.
2. A
Stunted means stopped “short or canceled abruptly.” Answer choice (A)
halted also means “stopped short.” Remembered real-life context may
be helpful here as well. If you have ever heard that someone’s “growth
was stunted,” something prevented that person from growing as much
as he
otherwise might have.
3. B
While a sturdy home might be huge, it does not by nature have to be.
Something sturdy, however, would be considered strong. Choice (B) is
the most accurate answer.
4. B
Undeterred uses the prefix un–, meaning “opposite of,” with the root
word “deter.” To deter something is to stop or hinder it. So something
undeterred would be something unhindered or persistent.
5. C
Ennui derives from a French word meaning boredom or “listlessness.”
Choice (C) is correct.
6. A
Mutable means “prone to change.” Consider the word root mut, which
appears in mutant (something or someone changed from the norm).
Choice (A) changeable is the best answer.
7. C
To squander is to “waste or fritter away” something. Of the choices
given, only (C) wasted means the same. This is a good question on which
to use context to eliminate some of the choices. There’s nothing
necessarily shameful about (A) gathering or (D) owning money. Stealing,
choice (B), is certainly shameful, so at that point you may have to make
a 50-50 guess. Or you could use another tool, like remembered real-life
context. It is unlikely you have ever heard “squander” on the news in the
context of a story about the .
8. A
You could use context on this one: handwriting is more likely to be
described as unreadable than as unethical or dangerous. A written work
might be creative, but handwriting refers to the way the letters are made
and not to the content of the writing.
9. B
The word infinite means “lasting forever” or unending. Break the word
into parts: in– means not, and the word root fin relates to ending. (Think
about final, finite, or finish, all of which relate to ending.)
10. B
Longevity means the length of time of a life or project, so choice (B)
duration is correct. The word part long relates to length, so look for an
answer choice that also relates to length.
11. A
Remember where you have heard “to fall for” used before. One “falls
for” a trick. Answer choice (A) is correct.
12. C
To proclaim is to announce or decree, especially in regards to a
prominent figure like a president. Think about word parts: pro– means
in front or before and claim is an English word meaning state or assert.
To proclaim therefore means something like “state in front of.” Answer
choice (C), announced, is a synonym for the given word.
13. A
Rudimentary means simple or easy. Of the answer choices given, only (A)
basic applies to something simple or rudimentary. On this question, try
rereading the sentence in your mind and substitute each answer choice.
When you do so, choice (A) makes the most sense.
14. B
The word rout means to “defeat soundly” in battle or competition. You
may have heard it in the context of stories about sports on the news.
Answer choice (B) is correct.
15. C
A rogue is someone who does not play by the rules. Use context: the
sentence draws a contrast between the idea of a team and the idea of
rogue. Answer choice (C) most directly contradicts the idea of teamwork
or team spirit.
16. C
Resonate has the word root son, which relates to sound, and the prefix
re– which means again or back. So resonate means something like
“sound again” or “sound back.” From there, you could think about
which answer choice both fits that meaning and fits the context.
Irritation, (A), and discussion, (D), do not seem to fit with the idea of
sounding back. Choice (B) doesn’t make any sense in the context. (In
fact, to resonate in music means “to have a full sound that seems to
reverberate.” In other contexts, resonate has come to mean
“harmoniously correspond” or “generate agreement.”)
17. A
Redundant starts with the prefix re–, or again. The first choice you have
available is repetitive, which means again and again. Context is also
useful here: the sentence suggests that redundant has something to do
with duplicating.
18. B
Prescribe means to “state authoritatively or “recommend.” Remembered
real-life context may be useful here. Think about when your doctor
prescribes a medicine: she is urging you, with some authority, to take
the medicine.
19. D
Logical means “based on logic” or “sensible.” Answer choice (D) is the
only choice that has anything to do with logic. If you weren’t sure what
sensible meant, you could have used remembered real-life context.
Think about the phrase “sensible shoes,” which are shoes that display
good sense or judgement on the part of the wearer.
20. A
Note that choice (A) requirement has the same root as the given word. A
prerequisite is something that is required before a project or course of
study begins. Answer choice (A) is correct.
21. A
Gravitate is based on a word it looks like: gravity. Even if you didn’t know
that gravitate means “moving towards,” you might be able to make a
guess based on the knowledge that the force of gravity pulls things
closer together. Choice (A) is correct.
22. D
Cautious means careful. Mentally rereading the sentence with each
answer choice substituted for the underlined word would likely have
been helpful here.
23. C
The meaning of braggart is “someone who brags.” While many (B)
leaders might brag, the correct answer choice here is (C) boaster (one
who boasts).
24. A
Hearsay is a term o en used in law. It means “secondhand stories”:
literally, what someone has heard someone else say. A rumor is a story
that has been heard from others without proof. Choice (A) is correct.
25. C
To taunt is to ridicule or tease. Even if you didn’t remember a context in
which you’ve heard the word taunt, you might have a sense that it has a
negative charge. Only choice (C) also has a negative charge.
26. B
The term constructive criticism refers to criticism that constructs or
builds up the listener rather than destroying her. Think of the word
construction, which means building. While (D) flattering words might
build some people up, flattery contradicts the idea of criticism. The
correct answer here is choice (B) productive.
27. C
To quantify something is to “be able to count” it. Think about the root
quant, which relates to numbers and which gives us the word quantity,
or amount.
28. C
Remembered real-life context might be helpful here. If you think about
where you have heard the word effective, advertisements for cosmetics,
drugs, and supplements might come to mind. Now ask yourself: what do
the companies who sell cosmetics or drugs want to tell us about those
products? They’re most likely to want to tell us that their products are
useful, productive, or successful.
29. C
Apathy means the state of not caring or disinterest. Think about word
parts: the prefix a– means not, and the word root path relates to feeling.
Think about sympathetic, which means sharing the feelings of others.
Thus, apathy means something like the state of not entering into others’
feelings, or disinterest.
30. B
A blemish is a glaring problem or defect. Try mentally rereading the
sentence with each choice substituted. You wouldn’t describe an (A)
impact as glaring, so that one is out. Moreover, glaring has a negative
context that does not fit with (C) commendation or (D) compliment.
31. A
Consensus has a root of con– meaning “with” (don’t confuse this with
con– meaning
not). Only answer choice (A) suggests togetherness. Another way of
tackling this question is to read the sentence carefully and glean that to
get a measure passed, one would need agreement, not (C) infighting
(that is, fighting within a group). (A) is the correct answer.
32. D
Think about word parts: dis– means “not.” The word root sent relates to
perceiving or feeing and also appears in the word consent, which means
agreement. Thus, you can guess that dissent is the opposite of
agreement. Even if you don’t know what insubordination means, you
can eliminate the other choices because none of them suggest the
opposite of agreement.
33. D
Tempo means “the speed of something.” Remembered real-life context
might be helpful here: if you have heard the word tempo, it was likely in
a discussion about music. And it makes far more sense to say that music
has a speed than to say that it has a heartbeat, safety, or modernity.
34. B
Try to fit some of the words into the sentence given to test their context.
Glee and protection may be tempting at first glance, but neither fit the
construction of the sentence if you replace them for the word solace. But
comfort, (B), would make her feel better.
35. B
Pitfalls are “traps and problems that await.” Try mentally rereading the
sentence and substituting each choice. While climbers might experience
(A) joys and probably do work with (C) ropes, neither of those ideas
relate specifically to inexperienced climbers.
Answers and Explanations
PART 4: PARAGRAPH COMPREHENSION (PC)
1. A
This is an Inference question, so the correct answer may be implied but
not spelled out directly. The first paragraph talks about the participants
of urban legends. It turns out that those participants can never be
found.
2. D
This is an EXCEPT question, so the correct answer is the one that does
not characterize successful urban legends. If you were able to determine
that urban legends are fictional, then choice (D), a basis in reality, is
clearly the correct answer. Otherwise, you could use the process of
elimination on the wrong answer choices. The passage states that urban
legends “persist both for their entertainment value and for the
transmission of popular values and beliefs,” so choices (A) and (B),
which paraphrase this, are wrong. Finally, the very first sentence
describes urban legends as a new form of folktale, so (C) is out.
3. B
The author, while maintaining that there were other scientists with
similar evolutionary ideas, notes toward the end that Darwin’s
eloquence and his ability “to account for many diverse examples”
helped him establish his theories as the benchmark by which others
stacked up. Thus, choice (B) is correct. None of the other choices are
supported by the passage.
4. B
In questions that ask about the author’s tone, beware of answer choices
that exaggerate the author’s point of view. Choice (B) is correct because
the passage merely conveys relevant facts about an issue. While the
author does describe two opposing reactions that parents have had to
the changes that have taken place in elementary schools, no preference
is implied. Therefore choices (A) and (C) are incorrect. Be cautious with
choices such as these that use extreme language.
5. D
Although the wording of this question indicates that this is an Inference
question, the correct answer choice, (D), can be taken directly from the
first sentence. If most life is “dependent on organisms that store radiant
energy from the Sun,” it is dependent on light from the Sun. Remember
that on Inference questions you are looking for the one answer that
must be true based on what is stated in the passage.
6. A
The first paragraph describes ecosystems that are dependent on
photosynthetic organisms, while the second paragraph describes
ecosystems that are dependent on chemosynthetic organisms. In both
cases, the organisms serve similar functions as primary producers
within their different food chains, so choice (A) is correct. Choice (B) is
wrong because only chemosynthetic organisms are described in the
passage as supporting higher organisms “at great ocean depths.” (C) is
wrong because chemosynthetic organisms do not rely on sunlight for
their basic source of energy. Choice (D) is never discussed in the
passage.
7. D
The last sentence of the passage implies that Halley accurately
predicted the 1758 appearance of the comet. Thus, you can infer that
the appearance of the comet confirmed Halley’s theory and accorded
with his calculations.
8. D
The passage discusses a few ways to distinguish a crocodile from an
alligator. The first and most easily observed of these is the fact that the
crocodile’s head and jaws are longer and narrower. In other words, it has
a narrower snout, choice (D). (A) is out, because the animals’ mouths do
not necessarily have to be closed to distinguish one from the other.
Choice (B) is out because both animals can be found in the Everglades
National Park, and (C) is never discussed as one of the ways to
distinguish one giant reptile from the other.
9. A
On this question you are asked to infer what the agent believes. She
must assume that certain actors are inappropriate for certain parts,
because if she didn’t believe this her conclusion would make no sense; it
wouldn’t be possible for an actor to audition for an inappropriate part.
The actors’ talent, (B), isn’t questioned by the agent; she focuses on the
types of roles. The possibility that an actor’s appropriateness for the
part may be difficult to predict, (C), is never assumed by the agent; in
fact, if anything, such a belief would weaken her conclusion. Major roles,
(D), are never discussed in the passage.
10. A
To answer this Detail question, scan the passage for a reference to foot
or feet. The first such mention is in the second sentence, which states:
“Pentameter refers to the number of feet, or groupings of syllables.” So a
foot is just that, a grouping of syllables, choice (A).
11. D
This is a Global question, so reading the passage for details is not
necessary, although paying attention to the overall effect of those
details is. The author notes that public opinion on the war was swayed
when the Lusitania was attacked, prompting increased military
involvement from the United States. Choice (D) is a paraphrase of this
main idea. Of the wrong answer choices, (A) distorts a detail found in the
passage, implying a causal link between America’s support for Britain
and France and Germany’s sinking of the Lusitania that is not supported
by the passage. Choice (B) refers to a minor detail in the passage, and
choice (C) is simply not true according to the passage, particularly a er
the sinking of the Lusitania.
12. D
In this Inference question, you are asked to supply a conclusion that is
best supported by the passage. The author seems to believe that critics’
opinions aren’t necessarily more significant than those of the average
person, so (D), which restates this idea, is a valid inference. Though the
author says the critics’ opinions aren’t more valid than those of average
moviegoers, he doesn’t imply (A), that the critics’ opinions are usually
incorrect. Choice (B) is out because the author does not say that the
critics’ judgments are meaningless—merely that critics don’t always
make the right judgments. And the passage doesn’t state how frequently
critics dislike popular movies, (C).
13. C
This Detail question asks why Americans did not start using the tomato
until the mid-nineteenth century. According to the passage, the English
considered the tomato poisonous, and this myth continued to hold
sway in America until the mid-nineteenth century. In other words, they,
too, believed it to be poisonous, choice (C). None of the other answer
choices are supported by the statements in the passage.
14. B
The word “drowsy” is used to describe Daria. In the following sentence,
you learn that Daria looks forward to going to sleep each night. From
this information, you can determine that “drowsy” means tired or
sleepy. Nothing in the passage suggests that Daria was drunk, (A).
Throughout the passage, Daria is presented as the opposite of (C) happy
and (D) satisfied.
15. A
The author discusses how she enjoys escaping the sun by sitting under
the variety of trees in the forest. This implies that the trees provide
adequate shade for her enjoyment as stated in choice (A). Choice (B) is
the opposite of the meaning the author conveys. The author is thankful
for the shade from the trees, so it’s not accurate to say they are
impairing her enjoyment, (C). While it may be true that trees provide a
home for many animals, this concept is never discussed or implied in
the passage, so choice (D) is incorrect.
Answers and Explanations
PART 5: MATHEMATICS KNOWLEDGE (MK)
1. D
Use FOIL to solve:
(3x + 4)(4x− 3)
= (3x)(4x) + (3x)(−3) + (4)(4x) + (4)(−3)
= 12x2− 9x + 16x − 12
= 12x2 + 7x − 12
2. A
Pick numbers to solve this one. If n = 2, the tree grew 5 feet, or 60 inches,
in 2 years, which means it grew at a rate of 30 inches per year. Plug in 2
for n into the answer choices, and only (A) gives the target number, 30.
3. D
If the perimeter of ABCD is 56, then half that, or 28, is the sum of the
length and the width, since the perimeter of a rectangle = 2(length +
width). If AD = 16, then AB = 28 − 16 = 12, and the area of ABCD must be
16 × 12 = 192.
4. A
A square is a rectangle with four equal sides. Choice (B) may be
tempting, but in fact, any two opposing sides of a square are parallel. It
would be inaccurate to say that a square has four sides, all of which are
parallel. Choice (D), curvilinear, means “curved” and is not correct.
5. D
The question gives two inequalities here: a < b and b < c, which can
combine into one, a < b < c. Go through the answer choices to see which
must be true. If you add the corresponding sides of these inequalities: a
+ b < c + c, or a + b < 2c. This statement is always true, so it must be the
correct answer.
This question could also be approached by picking numbers. That might
look like this:
Choose a = 2, b = 3, and c = 4, to conform to the information in the
question stem. Now try each choice to see whether it is a true statement
about those numbers:
(A) 3 + 4 < 4 No way! Incorrect.
(b) 2 + 3 < 4 Also not true. Incorrect.
(c) 2 − 3 < 3 − 4 Nope. Incorrect.
(d) 2 + 3 < 8 Definitely true. This choice is correct.
If more than one answer choice had produced a true statement, you
would have tried again using different numerical values until you had
only one true statement.
6. C
Since the angle marked x° and the angle marked y° together form a
straight angle, their measures must sum to 180°. Substitute in 2z for x
and 3z for y, and solve for z:
7. B
There are 360 degrees in a circle and 60 minutes in an hour, so you could
solve this question by setting up a proportion in which n is the number
of minutes
Then cross-multiply and reduce the fraction:
8. C
The area of a triangle is
9. B
Since lines p and q are parallel, use the rule about alternate interior
angles. The angle marked y° is supplementary to a 65° angle, so y = 180 −
65 = 115.
10. A
You could either turn the percentages into decimals and multiply: 0.15 ×
0.15 × 200 = 0.15 × 30 = 4.5 and get the answer (A), or you could take it
one step at a time. 15% of 200 is
. 15% of
30 is
.
11. B
Don’t fall for the answer choice trap and assume that the average of
and
is
. Instead, use the average formula:
In this case:
.
12. C
This question is testing your knowledge of definitions. The supplement
of an angle is the angle that when added to the original angle equals
180°. So if an angle measures y°, its supplement is 180 − y.
13. B
If Diane has
of her room still to paint, she’ll need
or 5 more
cans to do the job.
14. D
You can’t find the value of either variable alone, but you don’t need to.
Rearranging the equation, you get:
15. C
When you multiply terms that have exponents over the same base, you
add the exponents and multiply the coefficients:
3x2 × 5x3 = (3 × 5)x2 + 3 = 15x5
16. D
You can pick numbers to make sense of this geometry problem. You are
asked to increase the sides of a square by 10%, so you want to pick a
number for the original sides of the square of which it’s easy to take
10%. For instance, you could say that the original square is 10 by 10.
10% of 10 is 1, so the dimensions of the increased square are 11 by 11. In
this case, the area of the original square is 100, and the area of the new
square is 121, which represents a 21% increase.
17. B
If
, then m = 15 × 2 = 30
Plug 30 in for m to solve the expression asked for in the question:
18. C
To factor 6x2 − 13x + 6, you need a pair of binomials whose “first” terms
will give you a product of 6x 2 and whose “last” terms will give you a
product of 6. Since the middle term of the result is negative and the last
term is positive, the two last terms of the factors must both be negative.
One of the factors is among the answer choices, so you can use the
answer choices in your trial-and-error effort to factor. You’re looking for
a factor with a minus sign in it, so the answer’s either (C) or (D). Try (C)
first: Its first term is 3x, so the other factor’s first term would have to be
2x (to get that 6x 2 in the product). (C)’s last term is −2, so the other
factor’s last term would have to be −3.
Check to see if (3x − 2)(2x − 3) works:
(3x − 2)(2x − 3)
= (3x)(2x) + 3x (−3) + (−2)(2x) + (−2)(−3)
= 6x2− 9x− 4x + 6
= 6x2−13x + 6
It works. There’s no need to check (D).
19. D
Just be careful and translate the English into math: “the product of 3
and x is equal to 2 less than y ” becomes 3x = y − 2. But all of the
equations in the answer choices set the right side of the equation to
zero, so do that to your equation:
3x = y − 2
3x − y = −2
3x − y + 2 = 0
20. A
Since
is the reciprocal of
well. Combine the terms in
,
must be the reciprocal of
as
and then find the reciprocal:
Therefore,
21. C
This figure is an unfamiliar solid, so don’t try to calculate the volume
directly. The question says that the solid in question is half of a cube.
Imagine the other half lying on top of the solid, forming a complete
cube.
Notice that the diagonal with length
and two of the cube’s edges
form an isosceles right triangle. In an isosceles right triangle, the
hypotenuse is
times the length of a leg. Here the hypotenuse has
length
, so the legs have length 4. Thus, the edges of the cube have
a length of 4. The volume of a cube is the length of an edge cubed. So
the volume of the whole cube is 4 × 4 × 4, or 64. The volume of the solid
in question is
of this, or 32.
22. B
Begin by writing the division problem as a fraction:
. Now
move the decimal points on the top and the bottom of the fraction the
same number of places to the right until you are dealing with whole
numbers:
. Now divide:
.
23. B
The circumference of a circle = 2π(radius), so
.
The circumference is 8:
The area of a circle = π(radius)2, so the
area of a circle with a radius of
is:
24. B
You could translate the English into math to get:
.36 × 18 = .18 × n
However, you don’t have to go through all that work if you realize that x
percent of y = y percent of x.
25. C
Here you’re looking for an extremely rough approximation (the answer
choices all have a range of 100), so square the upper bounds of the
ranges in the answer choices, until you find the range that encompasses
104,906. Start with the upper bound of (A): (200)2 = 40,000, which is less
than 104,906. Now try (B): (300)2 = 90,000, which is still too low. Now
check (C): (400)2 = 160,000. 104,906 is between 90,000 and 160,000, so
(C) is the correct answer.
Answers and Explanations
PART 6: ELECTRONICS INFORMATION (EI)
1. B
Resistance is measured in ohms, and the symbol for an ohm is Ω
(omega).
2. B
Two types of particles are found within the nucleus: protons and
neutrons. Protons have a positive charge, and neutrons are neutrally
charged.
3. A
Alternating current (AC) is when the electric current reverses direction
many times in a second.
4. D
This symbol represents a short circuit, which is an accidental path of low
resistance that passes an irregularly high amount of current.
5. B
I represents current. Current is the rate of flow of electrons, or the
Intensity of the flow. (Specifically, I is the rate of charge flow.)
6. D
The P-type material in a diode is the anode, and the N-type material is
known as the cathode.
7. D
Pure silicon must be doped in order to generate holes or free electrons.
This process creates the P and N materials needed to make diodes and
transistors.
8. A
Capacitors stop direct current flow but not alternating current. The
higher the frequency of an alternating current, the less resistant effect a
capacitor has. Standard resistors, both fixed and variable, definitely
resist AC flow, as do inductors.
9. D
When wired in series, the resistance of several loads can be added
together to determine the effective resistance. The sum of the four
resistances is 20 Ω.
10. C
The arrow in a transistor symbol is always placed on the emitter, and the
arrow always points toward the N-type material at that junction.
11. A
This is the circuit symbol for a voltmeter, which is used to measure
voltage.
12. B
There are three essential components of an electrical circuit: a voltage
source, a load, and conductors to connect the load to the voltage
source. When these three components are connected so that current
can flow, it is a closed circuit.
13. A
A doorbell is typically operated by a push switch, which allows current
to flow only when a button is pressed. (A) is the symbol for a push
switch.
14. B
This is the schematic symbol for an alternating current (AC) voltage
source.
15. C
Capacitors that are electrical storage units are also known as
condensers.
16. C
An insulator is a material that does not conduct electricity.
17. A
Rubber is an example of an insulator. All of the other examples in this
question are conductors.
18. C
Four 6-ohm resistors wired in series will have a total resistance of 24
ohms. Using I = V ÷ R, a total of 0.5 A will flow in this circuit. 0.5 A is the
same as 500 mA.
19. A
The term semiconductor refers to an element that has four electrons in
its valence shell. Since the bonds between these four electrons and the
nucleus are somewhat strong, these elements are neither good
conductors nor good insulators. One element that is widely recognized
as a semiconductor is silicon.
20. D
This is the circuit symbol for a galvanometer, which is used to measure
extremely small currents, usually of 1 mA voltage or less.
Answers
and Explanations
PART 7: AUTO AND SHOP INFORMATION (AS)
1. D
While a miter box might be used with a backsaw to make even cuts in
wood at specific angles, by itself, it is not capable of shaping wood. All of
the other choices are tools capable of making cuts or smoothing edges
on wood.
2. B
Of all the aspects of vehicle operation, two that are a high priority for
most drivers are ride comfort and handling. The suspension system,
choice (B), is responsible for the ride quality of the vehicle.
3. D
The cut or slot le by a saw in a piece of wood is also known as a kerf.
4. D
The transfer case is located between the transmission and the drive
axles on a four-wheel drive vehicle and is the piece that splits the
engine’s power between the front- and rear-drive axles.
5. B
This is a crosscut saw. It is designed to, as its name suggests, cut across
the grain of the wood. Crosscut saw teeth are unique in that they cut like
a knife, in contrast to a ripsaw, which is made to cut with the grain of
wood.
6. C
This image depicts the compression stroke, which is the second stroke
in the four-stroke cycle.
7. A
Fractional measurement fasteners (measured in fractions of inches) use
threads that are identified by the number of threads per inch.
8. D
To loosen tight fasteners, it is good to use a box-end wrench. Choice (B)
depicts a combination wrench, which has an open end wrench on one
side and a box end on the other. Choice (C) shows a wrench with box
ends on both sides. Therefore, both (B) and (C) are suitable for loosening
tight fasteners; choice (D) is the correct answer. The box end wraps
completely around the head of a bolt, and therefore makes greater
surface contact.
9. A
Of the answer choices given, only (A), coil spring, is not a part associated
with the steering system. Coil springs are what aid the wheels in moving
up and down while the vehicle chassis stays steady. The other pieces
listed—steering knuckle, tie rod end, and idler arm—are all parts of the
steering system.
10. C
The camsha , indicated in the diagram by the number 3, is responsible
for the opening and closing of the engine’s intake and exhaust valves.
The camsha turns at one-half the speed of the engine’s cranksha .
11. D
In fuel-injected engines, the electric fuel pump is located in the vehicle’s
fuel tank and is what supplies fuel under pressure to the fuel injectors.
12. B
The two basic thread classifications—Unified National Coarse (UNC), and
Unified National Fine (UNF)—have different numbers of threads per inch.
A UNC or coarse thread would have relatively few threads per inch,
where a UNF or fine thread would have a larger number of threads per
inch.
13. C
Power brake systems use both the engine intake manifold vacuum and
fluid pressure from the power steering system to increase pressure.
Engine intake manifold vacuum is utilized to generate greater force on
the master cylinder, so higher hydraulic pressures can be generated in
the brake system. Some brake booster systems use fluid pressure from
the power steering system to increase braking power.
14. D
The primary is the low-voltage part of the system and contains a battery,
an ignition switch, a primary coil winding, an ignition module, a reluctor
and pickup coil, and a -distributor. A rotor is not a part of the ignition
primary system.
15. A
Stoichiometric is the ideal ratio of air to fuel in the engine and it is the
responsibility of the engine’s fuel system to maintain this balance.
16. D
Viscosity is resistance to flow, and is expressed as a number that is
directly proportional to the thickness of the oil.
17. C
Because they serve different purposes within an automobile, both
negative ground current and direct current electrical systems are
incorporated into cars.
18. D
Stick welding involves the use of an electric arc welding machine and
two cables: one that attaches to the work being welded through a
ground clamp, and the other going to an electrode that is sometimes
referred to as a -stinger. For safety reasons, always clamp to the work.
19. D
The last major cylinder arrangement that has been utilized by engine
designers is the horizontally opposed or flat design. This has all of the
cylinders lying on the horizontal plane, with half of the cylinders facing
away from the other half and the cranksha located between them.
Some refer to this design as a “boxer” engine because the pistons move
back and forth like a boxer throwing punches.
20. B
The tool pictured is a dri . It is used for striking an object where it is
important that the hammer itself does not come in direct contact with
the work. A chisel normally has a long edge and is used for cutting, (A),
where a punch is narrow and is used for driving small fasteners and
making layout marks, (C). To guide a saw when cutting across the grain,
(D), you might use a miter box, but you would certainly not use a dri .
21. A
This design is known as single overhead cam or SOHC. In a V-type
engine with two cylinder heads, there would be two camsha s, with one
installed above each cylinder head.
22. D
Any air passing through to the car’s combustion chamber must naturally
pass through the intake port in the cylinder head, the intake manifold,
and the air filter. Since the intake valve is open and is allowing
atmospheric air to enter the combustion chamber, higher atmospheric
air pressure pushes air through the engine’s intake system and toward
the low-pressure area above the piston. As the air is traveling through
the intake system, fuel is injected into the air stream before it enters the
combustion chamber. Gases do not pass through the catalytic converter
until they are almost ready to be expelled from the car.
23. D
Since most nuts are smaller sized, and because the 6-point socket is a
stronger design, it is usually the mechanic’s first choice in the smaller
socket drive sizes. And a breaker bar attached to a socket can give
enough twisting force to loosen very tight fasteners.
24. D
This is an external hole-type retaining ring. Retaining rings (or snap
rings) are used to prevent end-movement of cylindrical parts in bores or
parts mounted on sha s. External snap rings are installed in grooves on
sha s, whereas internal snap rings install in grooves inside a bore. Snap
rings are installed and removed using snap ring pliers.
25. B
A car’s battery contains lead plates immersed in an electrolyte made up
of sulfuric acid and water. When the battery discharges energy, the
sulfur binds with the lead plates to make lead sulfate, and the
electrolyte is reduced to water. Even though water is a result of this
process, it is not true to say that (A) the lead plates release water,
because the water is already part of the electrolyte mixture.
Answers and Explanations
PART 8: MECHANICAL COMPREHENSION (MC)
1. A
The principle of conservation of mechanical energy says that the total
mechanical energy of an object (PE + KE ) remains constant as an object
moves. As the car rolls down the hill, its speed increases because its
potential energy (PE ) is being converted into kinetic energy (KE).
2. C
During the ball’s journey upward a er being thrown, the ball has its
maximum kinetic energy when it leaves the thrower’s hand. This kinetic
energy is converted into potential energy as it rises. Maximum potential
energy (PE ) occurs when the ball stops rising, and this is where its
velocity is zero.
3. B
Inertia is a function of an object’s mass. A large mass will require a large
amount of force to cause it to accelerate. The larger the mass, the
greater the inertia of the object. Momentum, (A), is a quality of an object
in motion and describes how difficult it is to change the velocity of a
moving object. Torque, (C), is a rotational force. Pressure, (D), is force per
unit area.
4. C
Isaac Newton discovered that every particle in the universe is attracted
to every other particle. This concept became a physical law known as
Newton’s law of universal gravitation. The gravitational force that each
body exerts on the other grows stronger as the bodies get closer. The
force also increases as the mass of the bodies increase.
5. D
Based on Newton’s second law, F = ma. Rearrange that equation to solve
for acceleration:
, where units of force are in Newtons and mass
is expressed in kg. Here:
6. C
Work is defined as force times distance. Li ing a box straight up to the
top of a ramp will require the same amount of work as pushing the box
up the ramp (neglecting friction). The ramp allows a smaller force to be
applied over a larger distance. However, the end result or net work done
is the same in both cases.
7. B
It is not possible to get more work out of a machine than what is put in.
Machines do not reduce work, they simply manage it and make it easier
by diminishing the amount of force that is required.
8. A
A chisel is an example of a wedge.
9. B
The wedge is a variation of the inclined plane, but is made to move
whereas the inclined plane is made to stay in one place.
10. A
The distance from post A to the load is less than the distance from post B
to the load; therefore, it holds the greater part of the load.
11. C
Work and kinetic energy are both measured in joules. This is not a
coincidence, as any work that is done to accelerate an object at rest will
be converted into the kinetic energy of that object. This principle is
known as the work-energy theorem.
12. B
A screwdriver gains mechanical advantage through the use of a large
wheel (screwdriver handle) rotating a small wheel (screwdriver tip),
much like a wheel and axle. Large movements converted into small
movements will amplify the force applied.
13. B
Any time that force is increased through mechanical advantage, there
will always be a proportional decrease in the distance moved.
14. A
A prybar can increase mechanical advantage, and can change the
direction of motion, so it is a first-class lever.
15. B
One horsepower is equal to 550 foot-pounds of work per second or 746
watts.
16. C
Moving the fulcrum toward the object will increase the force applied to
the object, but will decrease the distance that the object can be moved.
17. C
If a machine were able to produce more work than was put into the
machine, there would be a net increase in energy. This would violate the
laws of thermodynamics. The work put out by a simple machine can
never exceed the work put into it.
18. D
If a small gear drives a large gear, a speed reduction takes place. The
large gear will turn more slowly than the small gear and the speed of the
output will be slower.
19. B
A block-and-tackle requires a minimum of two pulleys, with a rope, belt,
or chain used to operate them. There is at least one fixed and one
moveable pulley in the block and tackle.
20. A
The force exerted to li an object using a single pulley is the same as the
weight of the object itself.
21. B
A doorknob is similar to a wheel and axle in that a large wheel (the
doorknob or handle) is used to operate a small wheel (the latch
mechanism).
22. A
Mass is a measure of the amount of matter in a substance. It does not
change from place to place. Weight, however, depends on the
gravitational constant, and does change depending on the location.
23. C
Consider “Torque” and “Speed” to be two people on a teeter-totter.
Whenever “Torque” goes up, “Speed” goes down, and vice versa. These
two quantities can be described as inversely proportional.
24. C
An object’s potential energy (PE) can be calculated using the formula
PE = mgh
where m is mass in kilograms (kg), g is acceleration due to gravity (9.8
m/s2), h is the height of the object in meters (m), and PE is gravitational
potential energy measured in joules (J).
25. A
No work is done because the box does not move. W = Fd, where F is force
(newtons), and d is distance (m). If an object experiences no change in
position, then no net work is done.
Answers and Explanations
PART 9: ASSEMBLING OBJECTS (AO)
1. C
2. A
3. D
4. B
5. D
6. C
7. A
8. B
9. C
10. D
11. B
12. C
13. A
14. D
15. B
16. A
17. C
18. D
19. B
20. B
21. C
22. A
23. D
24. B
25. C
ASVAB PRACTICE TEST B
ASVAB PRACTICE TEST B
PART 1: GENERAL SCIENCE (GS)
11
Minutes
— 25
Questions
Directions: In this section, you will be tested on your knowledge of
concepts in science generally reviewed in high school. For each
question, select the best answer and mark the corresponding oval
on your answer sheet.
1. Those wishing to reduce the “bad” cholesterol levels in their blood
should avoid
(A) polyunsaturated fats
(B) carbohydrates
(C) monounsaturated fats
(D) saturated fats
2. Water at sea level freezes at what temperature?
(A) 373 K
(B) 0°F
(C) 100°C
(D) 32°F
3. Which of the following subatomic particles has the largest mass?
(A) proton
(B) electron
(C) positron
(D) neutrino
4. Which of the following is an example of an autotroph?
(A) a vulture
(B) an apple tree
(C) a toadstool
(D) a sea anemone
5. The period from 4.6 billion years to 570 million years ago is called
the
(A) Phanerozoic eon
(B) Mesozoic era
(C) Paleozoic era
(D) Precambrian eon
6. Which of the following planets is larger than Earth?
(A) Mars
(B) Mercury
(C) Uranus
(D) Venus
7. When these fall into the Earth’s gravitational field, they are seen as
“falling stars.”
(A) asteroids
(B) meteoroids
(C) comets
(D) craters
8. The study of interactions between organisms and their
interrelationships with the physical environment is known as
(A) cytology
(B) ecology
(C) physiology
(D) embryology
9. Most absorption of nutrients from food happens in the human
body’s
(A) stomach
(B) pylorus
(C) small intestine
(D) large intestine
10. High tide occurs
(A) four times a year
(B) once a day
(C) once a year
(D) twice a day
11. Which is NOT a fact according to Newton’s Law of Gravitation?
(A) If the mass of the Earth were doubled, the gravitational force
on the Earth would double.
(B) The force exerted on the Earth by the Sun is equal and
opposite to the force exerted on the Sun by the Earth.
(C) If the mass of the Earth were doubled, the gravitational force
on the Earth would quadruple.
(D) If the mass of the Sun were doubled, the force it exerts on the
Earth would double.
12. Which of the following types of electromagnetic radiation has the
longest wavelength and lowest frequency?
(A) radio waves
(B) microwaves
(C) gamma rays
(D) visible light
13. The ratio by which light is slowed down by a medium is known as
the medium’s
(A) electromagnetic spectrum
(B) angle of incidence
(C) reflection
(D) refractive index
14. Which of the following has the highest pH?
(A) vinegar
(B) water
(C) baking soda
(D) cranberry juice
15. Foods rich in carbohydrates include all of the following except
(A) potatoes
(B) pasta
(C) fruits
(D) almonds
16. Members of an order are more alike than members of a
(A) class
(B) family
(C) genus
(D) species
17. The number of protons in the nucleus of an atom is its
(A) atomic symbol
(B) atomic weight
(C) atomic number
(D) atomic radius
18. The system of muscles that allows the lungs to expand and
contract, drawing air in and out is the
(A) diaphragm
(B) pharynx
(C) trachea
(D) bronchioles
19. The atom of an element with an atomic number of 17 must have
(A) 17 electrons
(B) 17 protons
(C) 17 neutrons
(D) an atomic mass of 17
20. Because mushrooms absorb nutrients from decaying leaves, they
are classified as
(A) autotrophs
(B) anaerobes
(C) saprophytes
(D) protozoans
21. The blood vessel with the LEAST oxygenated blood is the
(A) pulmonary artery
(B) aorta
(C) pulmonary vein
(D) arterioles
22. Saliva in the mouth begins the process of breaking down
(A) starch
(B) fat
(C) protein
(D) vitamins
23. In which of the following kingdoms do cells lack nuclei?
(A) Fungi
(B) Monera
(C) Plantae
(D) Protista
24. An atom that is not electrically neutral is called a(n)
(A) isotope
(B) positron
(C) ion
(D) allotrope
25. Which of the following is an example of a metamorphic rock?
(A) granite
(B) marble
(C) limestone
(D) shale
IF YOU FINISH BEFORE THE TIME IS UP, YOU MAY CHECK
OVER YOUR WORK ON THIS PART ONLY.
STOP
ASVAB PRACTICE TEST B
Part 2: Arithmetic Reasoning (AR)
36
Minutes
— 30
Questions
Directions: In this section, you are tested on your ability to use
arithmetic. For each question, select the best answer and mark the
corresponding oval on your answer sheet.
1. A certain machine caps 5 bottles every 2 seconds. At this rate, how
many bottles will be capped in 1 minute?
(A) 75
(B) 150
(C) 225
(D) 300
2. Jonah traveled 650 miles on his most recent trip and averaged 25
miles to the gallon. If gasoline cost $1.30 per gallon, how much did
he spend on his trip?
(A) $26.00
(B) $27.30
(C) $32.50
(D) $33.80
3. If there are approximately 3.86 liters in a gallon, and gasoline costs
$1.54 per gallon, to the nearest penny what is the cost of a liter of
gasoline?
(A) $0.35
(B) $0.40
(C) $0.44
(D) $0.47
4. How many minutes are there in one week?
(A) 3,600
(B) 7,200
(C) 10,080
(D) 86,400
5. Pat deposited 15% of last week’s take-home pay into a savings
account. If she deposited $37.50, what was last week’s take-home
pay?
(A) $56.25
(B) $112.50
(C) $225.00
(D) $250.00
6. If the ratio of males to females in a group of students is 3:5, which
of the following could be the total number of students in the group?
(A) 148
(B) 150
(C) 152
(D) 154
7. A car travels 288 miles in 6 hours. At that rate, how many miles will
it travel in 8 hours?
(A) 360
(B) 368
(C) 376
(D) 384
8. Martin’s average score a er 4 tests is 89. What score on the fi h test
would bring Martin’s average up to exactly 90?
(A) 91
(B) 92
(C) 93
(D) 94
9. In 2010, the population of town A was 9,400 and the population of
town B was 7,600. Since then, each year the population of town A
has decreased by 100 and the population of town B has increased
by 100. Assuming that in each case the rate continues, in what year
will the two populations be equal?
(A) 2019
(B) 2020
(C) 2027
(D) 2028
10. One number is 5 times another number and their sum is −60. What
is the lesser of the two numbers?
(A) −10
(B) −12
(C) −48
(D) −50
11. Jane gets paid $6.00 for each of the first 40 toy cars she makes in a
week. For any additional toy cars beyond 40, her pay increases by
50%. How much does Jane get paid in a week in which she makes
48 toy cars?
(A) $288
(B) $300
(C) $312
(D) $321
12. If a bora = 2 fedis, and a fedi = 3 glecks, how many boras are equal
to 48 glecks?
(A) 8
(B) 16
(C) 32
(D) 96
13. Nine temperature readings were taken, one reading every four
hours, with the first reading taken at 12 p.m. (that is, at noon). What
will be the time when the final reading is taken?
(A) 4 p.m.
(B) 8 p.m.
(C) 12 a.m.
(D) 8 a.m.
14. A school raised monthly tuition payments from $225.00 per month
to $300.00 per month. The percent of the tuition increase is which
of the following?
(A) 25%
(B) 33
%
(C) 66
%
(D) 75%
15. A truck going at a rate of 20 miles per hour takes 6 hours to
complete a trip. How many fewer hours would the trip have taken if
the truck were traveling at a rate of 30 miles per hour?
(A) 4
(B) 3
(C) 2
(D) 1
16. If a barrel has the capacity to hold 75 gallons, how many gallons
does it contain when it is
full?
(A) 45
(B) 48
(C) 54
(D) 60
17. If a salary of $45,000 is subject to a 40% deduction, the new salary
is:
(A) $18,000
(B) $27,000
(C) $30,000
(D) $36,000
18. 8! =
(A) 8
(B) 64
(C) 40,000
(D) 40,320
19. Fi een people chip in $40 dollars each to throw a birthday bash for
a mutual friend. If 35% of the money is spent on a group gi and
the rest is spent on the party, how much was spent on the party?
(A) $210
(B) $300
(C) $350
(D) $390
20. If an employee worked a total of 33
hours over five days, what was the average amount of time that
the employee worked each day?
(A) 6 hours, 35 minutes
(B) 6 hours, 40 minutes
(C) 6 hours, 42 minutes
(D) 6 hours, 45 minutes
21. If a train starting out at point A travels 180 miles at a rate of 60 miles
per hour and then 150 miles at a rate of 75 miles per hour before
arriving at point B, what was the average rate, in miles per hour, for
the entire trip?
(A) 66
(B) 67.5
(C) 68.5
(D) 70
22. A er being discounted by 20%,